Heat a large stock pot over medium-high heat. Cook and stir beef until browned and crumbly, 10 to 15 minutes; drain and discard grease. Mix beer, tomato sauce, diced tomatoes, pinto beans, red beans, kidney beans, 2 chopped onions, green bell pepper, red bell pepper, brown sugar, garlic, chili seasoning mix, cornstarch, and mustard into ground beef; bring to a boil. Reduce heat, cover pot, and simmer, stirring frequently, until flavors have blended, about 1 hour.
Top each serving with about 1 tablespoon Cheddar cheese, 1 1/2 teaspoons onion, and hot sauce; season with salt and pepper.