Bake the Toast: Preheat your oven according to the package directions on your frozen Texas toast. Bake the slices for 8 to 10 minutes until they are golden-brown and crispy.
Brown the Meat: While the toast bakes, heat a large skillet over medium-high heat. Add the ground beef, diced onion, and green bell pepper. Cook for 6 to 8 minutes, breaking up the meat with a wooden spoon, until fully browned and the vegetables are soft. Drain excess grease.
Aromatize: Return the skillet to medium heat, add the minced garlic, and stir constantly for 1 minute until fragrant.
Build the Sauce: Stir in the ketchup, tomato paste, brown sugar, Worcestershire sauce, yellow mustard, and beef broth until thoroughly combined.
Season and Simmer: Add the chili powder, garlic powder, salt, and black pepper. Lower the heat to medium-low and let the mixture simmer gently for 8 to 10 minutes, stirring occasionally, until the sauce is thick and glossy.
Assemble and Serve: Arrange the warm garlic toast slices on plates. Spoon a generous amount of the warm sloppy joe filling over each slice. Top with shredded cheddar cheese if desired, and serve immediately.