1. Cook the meat in a large skillet over medium to medium-high heat until it is no longer pink. Drain any excess fat if required.
2. Sauté diced onions and bell peppers in the skillet with the cooked meat until the vegetables are tender. Add minced garlic for an extra layer of flavor.
3. Season the mixture with garlic powder, salt, black pepper, brown sugar, and cayenne pepper. Stir in the ketchup, beef broth, mustard, Worcestershire sauce, and tomato puree or paste until everything is combined.
4. Thicken the dip by creating a slurry with equal parts cornstarch and water or by sprinkling in some flour. Stir continuously while allowing the mixture to simmer to ensure even thickening.
5. Add shredded cheese to the dip and stir until fully melted and incorporated. Reserve some cheese to use as a topping.
6. Allow the dip to simmer on the stovetop or bake it in the oven for a few minutes. If using the oven, broil at the end for a bubbly, golden-brown cheese topping.
7. Transfer the hot Sloppy Joe Dip to a serving dish and serve with your choice of dippers such as toasted baguette slices, tortilla chips, or raw vegetables.