raw != image
You have to realize that raw files are just data.
Interpreting that data in a certain way can lead to images.
Each photo editing software will interpret the data differently or even jsut display an embedded jpeg image. That's why the images I have do not look similar to what you have.
I did this with Lightroom 5 very quickly. I explain each setting I applied.
You posted a crop to illustrate the issue. I chose a different crop. Her right eye is at the top and left third of the image (rule of thirds)
In general, the first thing to fix is the overall exposure. But in this case, the hair and dress look all right. The face is overly bright. That's why I only reduced the highlights instead of adjusting the exposure in general. The result is a step in the right direction. A lot of the texture of the face is now visible. (only after this step did I notice the piercing)
More light? Yes! The exposure of the image is correct, but it lacks a bit of punch, i.e. contrast. To add contrast, I added more white until I found the white point. This is the point where the first areas in the image start to be pure white again. In the previous step I took a big step out of the overexposed danger zone and in this step I'm carefully sneaking back.
This is the black point. It is very similar to the white point, except that you adjust the blacks until parts of the image start to become totally black. I pushed this a little further than the white point, because I wanted to make the background entirely black. The image now looks a lot more vivid, because the contrast is increased. The hair is black again.
local adjustment on the face | highlights -100
The overall image now looks better, but I also added some light back into the overexposed areas. I now used the adjustment brush to locally reduce the brightness of the overexposed areas. The result is that the highlight areas get back a bit more detail and texture. If you want to reduce the brightness even more, pick a lower (darker) white point in the second step. The question is how much you want to recover the overexposed areas.
local adjustment on the face | clarity -40
Making the texture of a face more visible is usually an undesired effect. It is very debatable if, which and how such features of a face should be removed. Every photographer/retoucher will have their own opinion which might vary depending on the client. I reduced clarity to smooth out the face a bit. This is where I stopped editing the image and what I would call the final result.
areas of local adjustment
Depending on your monitor settings and environmental light, the differences introduced in the last two images might be hard to spot. They are more subtle than the thirst ones. I colored the areas that I applied the local adjustments to, to make it more clear.
facing the truth
I do not agree with "we can fix this in post", because
- The highlights can only be recovered to a certain extent and the image was very bright to begin with. I could have put more emphasis on recovering the overexposed areas, but that would not create a good overall image. This is a portrait and editing it should not be all about getting rid of the overexposed area that covers pretty much the entire face.
- The focus is on the nose, not on the eye(s). Take a look at the
following crop to the eye and the nose. You can see that the nose is
more in focus than the eye. For portraits, the focus should be on
the eye. this is something that you cannot really fix in post. You
can try to sharpen the eyes, but it won't be as good as the real