I'm looking for suggestion on what to grow on sloped lawn

I have a section of lawn that I really would like to avoid mowing. Its sloped and on a few occasions I've almost lost my footing. My plan is to remove the grass and plant something in its place that doesn't require such attention. My initial thought was a low growing variety of purslane. But I'm not too familiar with this plant and concerned about it being invasive. Does anyone else have suggestions/ideas on what to grow here. I live in CT and this section gets shade and sun. Thanks in advance.

Aaron, I have been racking my brain trying to figure out something for that area.

I LOVE purslane because it is one of the most amazing superfoods you can have in your yard. But my zone is so different from yours. Here purslane would not work as a ground cover all year long.

My preference is to have a plant that will serve multiple purposes such as groundcover/medicinal/edible/pollinator, etc. -- purslane would certainly fit in all four of those catagories. So the question remains - will it be a vigorous plant that will come back every year in your climate?

Thanks Jeanine for taking the time to help. I went for a walk today and I think I found something that I'll try-Common Plantain. It's edible as far as I know and doesn't seem to grow that high.

white clover...nice and low, pretty flowers, bees love it...

The purslane would likely leave so much soil exposed - I bet it would look pretty sloppy after a wet spring. Maybe have a pathway somehow...for best shade-tolerant fruits in your area - black currants (leaves get nibbled way less than reds or whites at my place) gooseberries..jostaberries...even a hardy kiwi against that wall if it gets some sun. Russian comfrey too...that will get things super lush - as would some rhubarb. Have fun with that it will look amazing.

Thanks Anthony for your reply. We're getting ready for winter but I think I decided to make more of an investment (labor, money) and terrace that section. I think with it being terraced I can do the things you suggested much easier as well as do other things.