First, heat a large skillet over medium-high heat. Add the ground beef and use a sturdy spatula to break it apart. As it starts to brown, continue to chop it into small, pea-sized pieces. This creates more surface area for browning and flavor.
After about 3 minutes, add the diced onion and bell pepper to the skillet. Keep stirring and chopping, allowing the vegetables to soften and absorb the beef fat. Once the beef is fully cooked, season generously with salt and pepper, then stir in the ketchup and optional hot sauce.
Gather the beef and vegetable mixture into an even layer in the pan. Place the American cheese slices directly on top, covering the entire mixture. Reduce the heat to low and cover the skillet with a lid for about one minute to let the steam melt the cheese into a perfect blanket.
While the cheese is melting, split your hoagie roll and toast it lightly. A quick toast in a toaster oven or face-down in the skillet works great. Spread mayonnaise on both halves of the toasted roll, then scoop the cheesy beef mixture onto the bottom half. Top with the other half of the roll and enjoy immediately.