You may build a few steps in the grassy area that you can use to reach the street level. I am assuming that the concern is walking on it. If the concern is cosmetic then there is not much you can do because the street level is much lower than your house and not enough horizontal length for the vertical drop.

I think it's beautiful. You might want to add some flowers for color.

it is not the only option. you could do pavers or a system of gravel stabilization. Pics taken from internet

You may want to have it properly paved. Is the damage done by snow/freeze/thaw action?