Preheat oven to 350℉. Line a baking sheet with non-stick foil.- and toast the buns, inside of the bun facing down, until toasted, about 10 minutes.
In a skillet, add in the olive oil over medium heat. Once hot, add in the onion, garlic, and bell pepper.
Cover and cook for 5 minutes, stirring occasionally, until onion is transparent.
Uncover and add in the ground meat. Cook for 7-10 minutes or until no longer pink. Drain our any excess liquid.
Stir in the ground mustard, brown sugar, Worcestershire sauce, chili powder, ketchup, and red wine vinegar, and red wine vinegar. Season with salt and pepper to taste.
Cover and reduce heat to medium-low. Cook for 5 more minutes.
Place the buns onto individual plates, pouring a generous scoop of meat mixture on top of the bottom bun and a slice of cheese on top. Close the sandwich with the top bun.
Serve with your choice of side.