1. Brown the beef in a large skillet over high heat. Drain off the excess fat.
2.Reduce heat to medium-high; add the onions, green peppers, salt and pepper. Sauté until the onions and peppers are softened, about 5 minutes.
3. Add the tomato paste, Worcestershire sauce, mustard, vinegar and brown sugar. Stir to combine. Add water until the sauce is the desired thickness. Reduce heat to medium-low; cover and simmer about 10 minutes so the flavors combine. Taste and adjust as needed.
4. Serve on buns, garnished with relish and/or mustard if desired.
Tip: Toast the buns for extra crispiness.