Step 1

In a large saucepan or Dutch oven over medium-high heat, add beef. Cook until beef is dark brown and caramelized on one side before breaking apart, about 5 minutes.

Step 2

Stir in green pepper, onion, and mushrooms and cook until softened, about 2 to 3 minutes longer.

Step 3

Meanwhile, in a small bowl whisk together ketchup, brown sugar, vinegar, Worcestershire sauce, and mustard.

Step 4

Pour sauce ingredients over drained beef and stir until evenly coated. Cover and simmer 20 minutes, stirring occasionally. Season to taste with salt and pepper.

Step 5

Meanwhile, preheat broiler on HIGH. Arrange split rolls on a baking sheet and broil until toasted, 30 seconds to one minute.

Step 6

Divide mixture evenly on the bottom half of each roll. Top with cheese and broil until the cheese is melted, about 30 seconds to one minute. Top with buns. Serve with mayonnaise if desired.