I'm going to take a wildass blind guess, but doing an image search on Google which led to WrongRob's Instagram and then his website, it looks like he shoots with a Leica M, which has a full frame sensor in it. So my guess would be that the thin depth of field may have been created with a Noctilux 50mm f/0.95 lens. Whatever apertures he's using, if he's shooting with a wide or normal lens at regular subject distances, he's using an extremely wide aperture: probably f/1.4 or wider.
I can only achieve a similar look using a 5DMkII with an adapted Olympus OM-mount Zuiko 50/1.2 wide open, and the other side effect of having such a wide aperture when shooting "available dark" means that you can gather enough light for the exposure to make things look like they're lit, when you're just using street lamp illumination. A 35/1.8 lens on APS-C can't achieve the same DoF unless used much closer to the subject, but at that point, would be unable to do the same framing. I don't think a telephoto lens was used--the perspective isn't "flattened" enough to my eye (well that and the fact that Leica street shooters tend to favor wide-to-normal lenses). The look is actually reminiscent of medium format. I might have wild-guessed Brenizer method, except falling snow would make that problematic.
The amount of background blur you get relies on a number of factors, of which aperture is possibly the least important, but the most easily controlled. These factors are:
camera to subject distance. The closer you are, the more blur you get. That's why macro shooters sometimes have to focus stack to get a deeper DoF, even stopped down into the f/16-f/22 range. This is, in fact, more important than sensor size, as you can see by shots of mine on full frame and on crop with the same 50/1.2 lens, wide open.
focal length. The longer the lens, the more blur you get.
subject-to-background distance. The farther away from the background the subject is, the more the background will blur.
aperture used. The larger the aperture, the more background blur you get.
A larger format sensor/film can appear to have a thinner depth of field, because to achieve the same composition as you would on a crop body, you'd either have to a) use a longer lens, or b) get closer to your subject, or both.