Heat a large skillet over medium heat. Add the ground beef and onion and cook for 6–8 minutes, breaking up the beef with a wooden spoon, until the beef is no longer pink. Carefully drain any excess grease from the skillet, if needed.
1 pound ground beef, 1 small onion
Add the garlic and cook until fragrant, about 1–2 minutes.
2 cloves garlic, minced
Stir in the ketchup, undrained diced green chilies, beef broth, chili sauce, chili powder, cumin, crushed red pepper, salt, and black pepper. Bring the mixture to a gentle simmer.
1 cup ketchup, 1 (4-ounce) can diced green chilies, ½ cup beef broth, ¼ cup chili sauce, 1 teaspoon chili powder, ½ teaspoon ground cumin, ¼ teaspoon crushed red pepper, ¼ teaspoon salt, ¼ teaspoon black pepper
Reduce the heat and simmer uncovered for about 15 minutes, stirring occasionally, until the filling has thickened. It should be thick enough to mound on a spoon without excess liquid pooling around it.
While the sloppy joe mixture simmers, preheat the broiler. Spread both sides of each slice of Texas toast with softened butter and arrange the bread on a baking sheet.
6 slices Texas toast, 2 tablespoons butter
Broil the bread for 2–3 minutes, or until lightly toasted. Flip the bread and broil for about 1 more minute, or until the other side is lightly toasted. Watch it closely because bread can burn quickly under the broiler.
Remove the bread from the oven and spoon about ½ cup of the sloppy joe mixture onto each slice. Top with the shredded cheddar cheese.
1 ½ cups shredded extra-sharp cheddar cheese
Return the baking sheet to the broiler for 1–2 minutes, or until the cheese is melted. Watch it closely to prevent burning. Serve immediately with Fritos or potato chips, if desired.