Brown ground beef in a large skillet over medium-high heat, stirring constantly until the beef is browned and is in small crumbles, about 10 minutes.
Stir in onion and green bell pepper; cook and stir until softened, 2 to 3 minutes.
Stir in minced garlic and sauté until fragrant and lightly cooked – not browned, about 30 seconds.
Add tomato sauce and stir, scraping the pan to dissolve any brown flavor bits from the bottom of the skillet.
Mix in ketchup, Worcestershire sauce, vinegar, brown sugar, Dijon mustard, salt, and black pepper.
Reduce heat to low and simmer, stirring occasionally, until the liquid has evaporated and the mixture is thick, about 40 minutes. ***At this point you could pour all of the mixture into a 6-quart slow cooker and set on low for 4 to 6 hours, or until ready to serve.
Season with more salt and black pepper, to taste if needed.