Heat a large skillet over medium heat and add the ground beef. Cook, breaking the beef into crumbles, until it is no longer pink and fully cooked. Drain any excess fat from the skillet.
Add the chopped onion, green bell pepper, and minced garlic to the skillet with the ground beef. Stir and cook for an additional 3-4 minutes until the onions and peppers have softened.
In a medium-sized bowl, combine the ketchup, water, brown sugar, tomato paste, yellow mustard, Worcestershire sauce, and chili powder. Mix well until all the ingredients are fully combined.
Pour the sauce mixture into the skillet with the ground beef and vegetables. Stir until the beef and vegetables are fully coated in the sauce. Lower the heat and let the mixture simmer for approximately 10-12 minutes, stirring occasionally. During this time, the sauce will thicken and the flavors will meld together.
While the Sloppy Joe mixture is simmering, toast the hamburger buns on the grill or in an oven/toaster until they are lightly browned.
When the sauce has thickened, season the Sloppy Joe mixture with salt and pepper to taste.
Cap off the cooking process by spooning an equal portion of the Sloppy Joe mixture onto the bottom halves of the toasted hamburger buns. Add your desired toppings such as pickles, cheese, or chopped onions.