In a large skillet over medium heat, cook the ground beef until browned, about 5-7 minutes. Break it up with a wooden spoon as it cooks. Drain any excess fat if needed.
Push the meat to one side of the skillet and add the diced onion and green bell pepper to the other side. Cook for about 3-4 minutes, or until softened. Add the minced garlic and cook for another minute until fragrant.
Stir in the gochujang, soy sauce, tomato paste, and brown sugar. Cook for 2 minutes, allowing the ingredients to blend together and the gochujang to release its flavors.
Add the Worcestershire sauce, ketchup, beef broth, and rice vinegar. Stir everything together until well combined. Let the mixture simmer over low heat for about 10 minutes, stirring occasionally. The sauce should thicken and coat the meat beautifully. If you prefer a looser sauce, add more broth or water as needed.
Taste the mixture and adjust the seasoning. Add salt, pepper, and smoked paprika if using. If you prefer it sweeter, you can add a bit more brown sugar or ketchup. For extra heat, a dash of hot sauce or more gochujang can be stirred in at this stage.
Toast your buns lightly on a skillet or grill for added texture (optional but recommended!). Spoon a generous portion of the spicy gochujang meat mixture onto the bottom half of each bun. Top with jalapeƱos, pickled onions, or coleslaw for extra crunch and freshness.
Top with the remaining bun and serve your Spicy Sloppy Joes immediately. Enjoy with a side of fries, chips, or a fresh green salad.