Preheat oven to 375°F (190°C).
In a large skillet over medium heat, cook the ground beef until browned. Drain excess grease.
Add diced onion and green bell pepper, cooking until softened.
Stir in tomato sauce, ketchup, Worcestershire sauce, garlic powder, and onion powder.
Simmer for 5-7 minutes, allowing flavors to meld. Season with salt and pepper.
Place Texas toast slices on a baking sheet and toast in the oven for 3-5 minutes until golden.
Spoon sloppy joe mixture over the toasted bread and sprinkle with shredded cheese.
Bake for an additional 5 minutes until cheese melts. Serve immediately.