Heat a large skillet over medium heat. Add the lean ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the chopped onion and cook for 3 to 4 minutes, until it starts to soften.
Stir in the minced garlic and cook for about 30 seconds, just until fragrant.
Add the drained beans to the skillet. Mash a few of them with the spoon if you want a thicker filling.
Stir in the tomato sauce, tomato paste, mustard, apple cider vinegar, Worcestershire sauce, chili powder, smoked paprika, salt, and black pepper.
Add the brown sugar only if needed. Start with 1 teaspoon, then taste after simmering.
Reduce the heat to low and let the mixture simmer for 8 to 10 minutes, stirring now and then, until the sauce thickens.
Taste and adjust the seasoning. Add a splash of water if it gets too thick, or simmer a little longer if it feels too loose.
Spoon the beef and bean mixture onto whole grain buns, open face toast, or into bowls.
Serve warm with a simple side like salad, cucumber slices, or roasted vegetables.