Melt butter in a large skillet over medium heat. Add ground beef and cook for 4-5 minutes, or until brown. If a lot of excess fat has accumulated in the skillet, spoon it out, leaving a tablespoon or so.
Stir in garlic and tomato paste, if using, and cook for another minute.
Add ketchup, water, brown sugar, chili powder, dry mustard, and Worcestershire sauce. Season with salt and pepper. Stir to combine and bring to a simmer.
Cover and simmer over medium-low heat, stirring once or twice, for about 15 minutes, or until liquid has reduced to your liking.
Taste and adjust seasoning, then serve on hamburger buns or rolls.