Dice the onion and green bell pepper into small pieces. Mince the garlic finely. Keeping the vegetables small helps them cook evenly and blend naturally into the beef mixture.

Heat olive oil in a large skillet over medium heat. Add the ground beef and cook until browned. Break the meat apart with a wooden spoon as it cooks.

Once the beef is fully browned, carefully drain excess grease from the skillet. Leaving a small amount of fat can help keep the mixture flavorful without making the sauce too heavy.

Return the skillet to medium heat. Add diced onion and bell pepper. Cook for four to five minutes until softened. Stir in the minced garlic and cook for another minute.

Stir tomato sauce, ketchup, and tomato paste into the beef mixture. Mix thoroughly so the tomato ingredients coat the meat and vegetables evenly.

Add brown sugar, mustard, Worcestershire sauce, chili powder, smoked paprika, salt, and black pepper. Stir well until the seasonings are spread throughout the mixture.

Pour in the water and stir everything together. Reduce the heat to low. Simmer uncovered for about 12 to 15 minutes, stirring occasionally as the sauce thickens.

The finished mixture should be thick and saucy. If it looks too dry, add one or two tablespoons of water. If it looks too thin, simmer for several additional minutes.

Lightly toast the hamburger buns in a dry skillet or toaster. Toasting adds a little crunch and helps prevent the buns from becoming too soft under the juicy filling.

Spoon the hot sloppy Joe mixture generously onto the toasted buns. Add cheddar cheese if desired. Serve immediately with your favorite side dishes for a warm and satisfying meal.