Preheat oven according to Texas toast package instructions, typically 425 degrees Fahrenheit.
In a large skillet over medium-high heat, brown the ground beef with diced onion and bell pepper until meat is cooked through and vegetables are softened.
Drain excess fat from the skillet and return the pan to the heat.
Stir in minced garlic and cook for 60 seconds until fragrant.
Add ketchup, yellow mustard, brown sugar, Worcestershire sauce, salt, and black pepper to the beef mixture.
Reduce heat to low and simmer for 10 minutes to allow the sauce to thicken and flavors to meld.
Bake the Texas toast slices on a baking sheet until golden brown and crispy on both sides.
Place each slice of toasted bread on a plate and top with a generous portion of the beef mixture and shredded cheese.