In a large skillet over medium heat, add the ground beef, diced onion, and green bell pepper. Cook until the beef is browned and the vegetables are softened, about 5-7 minutes. Drain any excess fat.
Stir in the ketchup, brown sugar, Worcestershire sauce, garlic powder, mustard, salt, and pepper. Mix thoroughly and let simmer for about 10 minutes, stirring occasionally.
While the beef mixture is simmering, toast the Texas toast in a toaster or oven until golden brown.
Once the beef mixture is heated through, taste and adjust seasoning if necessary.
To assemble, place a generous scoop of the sloppy joe mixture on a slice of Texas toast. If desired, sprinkle shredded cheddar cheese on top. Top with another slice of Texas toast to create a sandwich.
Serve immediately and enjoy!