In a skillet over medium heat, add the ground beef. Cook until browned, breaking it apart with a spoon as it cooks (about 5-7 minutes).
Drain any excess fat from the skillet and add the diced onion and green bell pepper. Sauté for about 3-4 minutes until the vegetables are soft.
Stir in the ketchup, yellow mustard, brown sugar, Worcestershire sauce, salt, and pepper. Mix well and let the mixture simmer for about 5-7 minutes, stirring occasionally.
While the Sloppy Joe mixture simmers, preheat another skillet or griddle over medium heat. Butter one side of each slice of Texas toast.
Place the Texas toast in the preheated skillet, buttered side down, and toast until golden brown, about 3-4 minutes. Flip and toast the other side until golden brown.
To serve, spoon the Sloppy Joe mixture generously over four slices of Texas toast and top with the remaining slices, buttered side up.
Optional: Serve with pickles and potato chips on the side.