Warm a large skillet over medium heat and add the olive oil. Stir in the onion and bell pepper.
Cook for 4–5 minutes until softened and lightly golden. Add the garlic and cook 30 seconds until fragrant.
Add the ground beef. Season with salt, pepper, paprika, and chili powder.
Cook, breaking up the meat with a spatula, until browned and no longer pink, about 6–8 minutes. Spoon off excess fat if needed.
Stir in ketchup, tomato sauce, brown sugar, mustard, Worcestershire sauce, and 1 tablespoon of the vinegar. Add 1/4 cup water or broth to loosen.
Reduce heat to medium-low and simmer 5–10 minutes, stirring occasionally, until thick and glossy.
Add more water or broth by the tablespoon if it gets too thick.
Taste and adjust. Add more salt if needed, another tablespoon of vinegar for extra tang, or a pinch more brown sugar for sweetness. The balance should be mildly sweet, noticeably tangy, and savory.
Serve hot on toasted buns with pickles and cheese, or spoon over rice or baked potatoes.
For a stovetop “sloppy mac,” fold in cooked elbow pasta and a handful of shredded cheddar.