I made a picture (see below) of an almond cake with the following settings:
I chose an appropriate shutter speed with the biggest aperture possible because I wanted to focus on the almond cake, blurring anything else.
If you look closer then you can see that the front part and the upper left part of the cake are kind of blurred also.
How can I avoid that? I'd like to have the cake focused as much as possible.
The short version is you need not the "biggest aperture possible" but the right aperture given the distance and desired depth of field.
There are a number of online depth of field calculators available (search for it, since these answers live a long time I hesitate to put specific links). Put in your focal length, distance, sensor information as appropriate (ones that do not ask about sensor will be less accurate). You should be given a depth in front, and behind the point of focus. Adjust aperture until you get something to cover the cake. Be sure to allow for finding a way to focus on a point in the middle (and note "middle" varies, but usually is closer to the front - you can tell by the results of the calculation). If you have a specific spot to focus on instead, say that upright corner, then be sure that both front and back area of focus reach all visible areas.
Then when you shoot, bracket your shots - take one shot with a smaller and one with a larger aperture. Or maybe two or three of each progressively smaller and larger, so you can pick the best.
Secondly you can stack the deck a bit. Use the longest focal length lens you have (at least that you can fit into your studio), provided it has a decently wide aperture. Also, place any background objects as far away as you can while maintaining whatever appearance you want. Objects with less edges will look more blurred. And in post processing, you can selectively sharpen the cake while masking off the background and not sharpen it (you can of course artificially blur it in post processing as well, but you will get different opinions whether such looks natural or not).
Finally, selectively lighting the target a bit (not a lot) brighter than the background will naturally fool the eye to add a bit more emphasis, adding to the separation from depth of field.
Your aperture is too wide for the shooting distance, focal length, and the magnification you are using to view your image. As a result only the center parts of the cake appear sharp and the extremes of the cake, both near and far, are slightly out of focus.
There's only one distance that will be in sharpest focus. Everything closer or further away from the camera will be blurry to one degree or another. The further away from the point of focus, the blurrier things will be. What we call depth of field is the distance within the area where the blur is not noticeable to our eyes. There's no magical line at which things on one side are equally sharp and on the other side are equally blurry.¹ It is a gradual transition from sharp to blurry. There are several variables that affect just how far from the point of focus things start becoming noticeably blurry to our eyes.
The blur becomes noticeable at smaller distances from the point of focus if we:
The blur increases more gradually at larger distances from the point of focus if we:
To properly calculate depth of field all of these factors must be taken into account. Many DoF calculators make (often unspoken) assumptions about some of them. Most DoF calculators, such as DOF Master, assume an 8x10 display size viewed from a distance of 10 inches by a person with 20/20 vision. Suppose one properly calculates the DoF from such a chart and then displays the image at both an 8x10 and a 16x20 size viewed side-by-side. The 8x10 print should demonstrate the calculated DoF, but the 16x20 print, viewed from the same distance, will have half the DoF of the 8x10 print!
How can this be?
In a way, depth-of-field is an illusion. There is only one plane of focus. Everything in front of or behind the point of focus is out of focus to one degree or another. What we call DoF is the area where things look, to our eyes, like they are in focus. This is based on the ability of the human eye to resolve certain minute differences at a particular distance. If the slightly out-of-focus blur is smaller than our eye's capability to resolve the detail then it appears to be in focus. When you magnify a portion of an image by making it larger or moving closer to it you allow your eye to see details that before were too close together to be seen by your eyes as separate pieces of the image.
Since things are gradually blurrier the further they are from the point of focus, as you gradually magnify the image the perceived depth of field gets narrower as the near and far points where your eyes can resolve fine details moves closer to the focal plane.
Keep in mind that when you are "pixel peeping" on your computer at 100% display, where one pixel in the image is displayed using one pixel on your monitor, you are viewing at the same magnification as if you are displaying the full image at a very large size. A 24MP image viewed at 100% on a 23" HD (1920x1080) monitor is the equivalent of a piece of a 60x40" print!
Here's an online depth of field calculator that gives the user the option of indicating display size and selecting desired visual acuity as well as entering focal length, aperture, and focus distance. Just click on the show advanced link to access all of the features.
¹Technically, if the blur is smaller than the resolution limit of the image sensor, then things will be equally sharp/blurry. But the pixel pitches of the vast majority of current digital sensors in cameras intended for creative photography are about 1/3 to 1/7 the width of the minimum blur we can see viewing an image created with those sensors at 8x10 display size from 10 inches away.
I chose a fast shutter speed and the biggest aperture possible because I wanted to focus on the almond cake, blurring anything else.
You're on the right track, but you overdid it. Use a slightly smaller aperture to add a little more depth of field, so that more of the subject is in focus. That will cause a slight decrease in the blurriness of the objects in the background, especially the baking dish. If you want to avoid that, put more distance between the subject and the background objects. For example, try keeping the distance between camera and plate the same but adding 12" or more between the plate and the baking dish.
I also shoot pictures like yours.
First, know the issue: put the cut face parallel with the picture plane, and don’t have the primary surface at an angle to you. You did the opposite: the cut edge varies in distance from the close point to the back.
I shoot additional f-stop values to make sure I got an acceptable shot. So if the plan is f/4 and I expect that should work, but after looking at them the cook says she doesn’t like the rest of the item blurring as it receeds, then I show her the f/5.6 version. If she still complains, then I can blur the table in Photoshop starting with the too-sharp one. I shoot an extra exposure at (say) f/11 just to be sure I have something in focus (for my APS-C camera, f/5.6 is optimal sharpness where it is in focus. Smaller apertures widen the DoF but the place of perfect focus is softer.)
With the gear you plan on using, shoot a test tableu to show the depth of field at different settings. I use dice. But use the same kind of plate, for context and scale. Knowing that, you can choose the still-life arrangement (“pose”) and know how much depth of field is needed, and know what to expect.
So, you know how much you can tilt the cake and still have the whole face sharp in focus, and coordinate the artistic aspects of the “pose” and the aperture. Worst case, shoot a series of pictures at different focus distances and use stacking software, or start with a super sharp exposure and add blur in Photoshop or from combining two exposures on different layers.
