Heat the oven to 350 F. Lightly coat a baking pan with cooking spray. Spray a frying pan with cooking spray.
Over medium heat, saute the peppers and onions until they soften, 3 to 5 minutes. Add the roast beef and saute for an additional 2 to 3 minutes.
Place 1/2 of the roast beef mixture on the bottom half of each bun. Place in the prepared baking dish. Top each bun with 2 tablespoons of the cheese. Bake until the cheese has melted, 2 to 4 minutes. Remove and add the top of bun and serve.