Preheat the oven to 425°F (218°C) or as specified by the Texas toast packaging.
In a 12-inch skillet over medium-high heat, brown the ground beef with the diced onion and bell pepper until the meat reaches an internal temperature of 160°F and the vegetables are translucent.
Drain the excess rendered fat from the skillet using a colander or slotted spoon.
Reduce the heat to medium-low and incorporate the tomato sauce, ketchup, brown sugar, Worcestershire sauce, mustard, garlic powder, salt, and pepper.
Simmer the beef mixture for 10 minutes, stirring occasionally, until the sauce has thickened and fully coated the proteins.
While the sauce simmers, arrange the Texas toast slices on a parchment-lined baking sheet and bake for 5 minutes per side or until golden brown.
Distribute the sloppy joe mixture evenly over the top of each toasted slice.
Grate the cheddar cheese and apply approximately 1/4 cup to each slice.
Return the baking sheet to the oven for 2 to 3 minutes until the cheese has achieved a complete melt and begins to bubble.
Remove from the heat and allow to rest for 2 minutes before serving.