In a large skillet over medium-high heat, cook 1 pound ground beef and 1 medium onion (diced), stirring occasionally, until the beef is browned, about 5 to 7 minutes.
Drain any excess fat from the skillet, then return the skillet to the heat.
Add 1 medium green bell pepper (diced), 2 ribs celery (siced), 1 (8 ounce can) tomato sauce, 1 (6 ounce can) tomato paste, 2 tablespoons Worcestershire sauce, 4 teaspoons minced garlic, 1 tablespoon brown sugar, 1 teaspoon salt, 1 teaspoon ground mustard, and 1/2 teaspoon crushed red pepper flakes. Stir well to combine all ingredients.
Bring the mixture to a simmer. Reduce the heat to medium-low and simmer uncovered for 30 minutes. Stir occasionally to prevent sticking.
Preheat the broiler on your oven and place the rack so that it is 12 inches beneath the broiler. Place 8 hamburger buns, open-face, on a baking sheet. Broil for 1 to 2 minutes, or until lightly browned. Keep a close eye on them to avoid burning.
Spoon the hot Sloppy Joe mixture onto the toasted hamburger buns. Serve immediately.