Place ground beef and onion in a large skillet. Turn heat to medium and cook and stir the mixture constantly until the beef is browned and forms small crumbles, about 10 minutes.
Stir in garlic and green bell pepper; cook and stir until softened, 2 to 3 minutes. Add 1 cup water and stir, scraping the pan to dissolve any brown flavor bits from the bottom of the skillet.
Mix in ketchup, Worcestershire sauce, brown sugar, Dijon mustard, salt, and black pepper. Add 1 more cup water and return mixture to a simmer. Reduce heat to low and simmer, stirring occasionally, until the liquid has evaporated and the mixture is thick, about 40 minutes.
Season with salt , black pepper, and cayenne pepper to taste.