Preheat oven to 425ºF.
In a large skillet, heat oil over medium heat.
Add onions and pepper and cook until tender.
Add ground beef and garlic and cook until ground beef is thoroughly cooked. Add mushrooms and cook until slightly tender.
Remove from heat.
Lay one wonton wrapper flat, add about 2 tablespoons of mozzarella cheese and 3 tablespoons of the beef/vegetable mix on top. Wrap wonton wrapper from one corner, followed by both sides toward the middle, then rolling the wrapper to form a roll (see images for details).
Add rolls to a baking pan coated with non-stick cooking spray.
Coat the top of each roll with olive oil or butter.
Bake for 15 minutes, turning rolls half way through.
To make cheese sauce, add butter to a sauce pan over medium-high heat.
Once butter is melted, whisk in flour, then milk, salt and black pepper.
Once sauce is thickened, add shredded cheese.
Serve immediately.