Place a large Dutch oven or saucepan over medium-high heat. Add the beef and cook until browned, about 5 minutes.
Add the onion, stirring well, and cook until translucent, 3 to 5 minutes. Add the garlic and cook for 1 minute more.
Gradually add the broth, scraping up any browned bits from the bottom of the Dutch oven; bring to a boil.
Stir in the chili powder, cumin, and tomatoes. Reduce heat to medium-low, cover, and let simmer for 10 minutes.
Add the beans, salt, and vinegar, stirring well. Simmer uncovered for 10 minutes more.
Serve with the Cheddar, sour cream, jalapeño, and corn bread, if desired.