Heat a large skillet over medium heat. Add the ground beef and cook until browned, breaking it apart as it cooks.
Add the diced onion and green bell pepper to the skillet. Cook until softened, about 3-4 minutes.
Stir in ketchup, tomato paste, Worcestershire sauce, brown sugar, and yellow mustard.
Reduce heat to low and simmer the mixture for 10 minutes, stirring occasionally, until thickened and saucy.
Meanwhile, heat a separate skillet over medium heat. Butter each slice of Texas toast on both sides.
Toast the buttered bread slices in the skillet until golden brown and crisp on both sides.
To serve, spoon the sloppy joe mixture generously over each slice of toasted Texas toast.
Serve immediately on white ceramic plates.