Prepare sauce to spread on each wrap by mixing together mayo and ketchup in a small bowl.
Saute peppers and onions in olive oil for 5 minutes. Add garlic and cook for 1 more minute. Remove from the pan and set aside.
Heat roast beef in the same pan for just about one minute. You don't want to overcook it.
Separate into individual portions and top with cheese to melt. Remove from the heat.
Wash and dry your lettuce leaves. Be gentle so that your lettuce doesn't tear.
For lettuce cups, spread some of your sauce on your lettuce. Scoop up the cooked meat with cheese and place in lettuce cups. Top with veggies. Then just pick them up and eat like you would a taco.
Or for an easy on-the-go wrap, layout two overlapping lettuce leaves on parchment paper. Spread some sauce onto the lettuce. Add your cheesesteak and veggies.
Now roll as tightly as you can tucking the ends of the lettuce inside. Then tightly roll your parchment paper around the lettuce wrap. Fold both ends tucking the paper in. Cut horizontally into two parts with a sharp serrated knife.
Tear off a little paper at a time as you enjoy eating your wrap.