Advice on rebuilding eroded area

I have an area between two houses that has for years lost a lot of soil due to water runoff from the front roof. That runoff is now resolved via gutters and a drainage pipe to the back, so now the struggle is what to do in building the terrain back up flat, best cover plants, etc.

The first thought is to just throw down some top soil to build it back up level and then grass seed, but I'm betting that's the wrong way to approach it, especially since it's now cooler and heading into winter. I could just wait until next year, but I'd like to repair what I can beyond just putting dirt down (which could still erode and be a mess).

The area had lost probably a few inches of top soil and grass from original construction, down to the clay substrate. There is some tree coverage as well, so it's partial shade which I know is problematic for good grass growth. I'm open to other cover plants, but it does have semi-regular foot traffic with landscapers, kids, pets, etc.

Is there a reasonably quick fix to do something?