Melt butter and garlic in a saucepan over medium heat; cook and stir onion into garlic until softened and lightly browned, 10 to 15 minutes.
Mix in soy sauce, Worcestershire sauce, chili powder, black pepper, paprika, white pepper, dry mustard, ginger, cayenne pepper, and thyme; cook and stir until combined, 1 to 2 minutes. Add brown sugar and let bubble for 1 minute.
Stir in chicken stock, ketchup, molasses, Dijon mustard, liquid smoke, and vinegar; simmer until thickened, 5 to 10 minutes. Cool and brush onto desired meat.