Heat butter and olive oil in a large skillet over medium heat.
Add ground beef, cook until browned, breaking it up with a spatula.
Drain excess fat if needed and set the beef aside.
In the same skillet, sauté minced onion, green bell pepper, and garlic until tender.
Stir occasionally to avoid burning.
This usually takes about 5 minutes.
Return the browned ground beef to the skillet and mix well with the vegetables.
Add tomato sauce, Worcestershire sauce, Dijon mustard, brown sugar, and ketchup to the skillet.
Stir until everything is evenly combined.
Season the mixture with salt and pepper to your liking.
Reduce the heat to low, and let it simmer for about 20 minutes.
Allow the flavors to blend well together.
Toast hamburger buns slightly if preferred.
Spoon a generous portion of the sloppy joe mixture onto each bun.
Serve warm and enjoy!