Preheat your oven to 425°F. In a large skillet, cook the ground beef with chopped green pepper, onion, and minced garlic over medium-high heat until the beef is browned and no longer pink, about 5-7 minutes. Break up the meat as it cooks, and drain off any excess fat.

Add the beef broth or red wine to the skillet and bring to a boil. Cook until the liquid is reduced by half, which should take around 2 minutes. Stir in the diced tomatoes, including their juice, and the tomato paste. Season with salt and black pepper. Bring the mixture back to a boil, then reduce the heat and let it simmer uncovered, stirring occasionally, until it thickens, about 2-3 minutes.

While the meat mixture is simmering, arrange the Texas toast on a foil-lined baking sheet. Bake in the preheated oven until the toasts are lightly browned, which will take about 8-10 minutes.

Once the toast is ready, spoon the beef mixture over each piece. Top with a slice of mozzarella cheese and return to the oven. Bake until the cheese is melted, approximately 3-4 minutes. Serve immediately.