Finely chop the onion and pepper, and mince or press the garlic. Or, save some time by quartering the veggies and pulsing them all in a food processor until very finely chopped.
Melt the butter in a medium skillet over medium-high heat. Add the ground beef and cook, breaking it up into small pieces with a wooden spoon or spatula, until it's no longer pink, 3 to 5 minutes.
Add the onion, pepper, and garlic and cook until the veggies are soft and fragrant, another 3 minutes or so.
Stir in the ketchup, water, brown sugar, Worcestershire sauce, mustard, chili powder, salt, and a few grinds of pepper. Turn the heat to medium-low and cook, stirring occasionally, for 10 minutes or until most of the liquid has evaporated and the sauce is nice and thick.
Scrape the sauce into a large bowl and let it cool on the counter while you prepare your dough and other toppings.