Char peppers over gas flame or under broiler about 10 minutes, turning often, until skin is completely blackened. Cover in a bowl with plastic wrap; steam 10 minutes.
Peel skin; remove seeds and stems, dice, and set aside.
Heat oil in a large pot over medium-high; brown beef about 8 minutes, breaking up with a spoon. Drain fat.
Cook onion about 5 minutes until soft; add garlic and cook 1 more minute.
Stir in chili powder, cumin, and coriander; cook 1 minute until fragrant.
Stir in roasted peppers, tomatoes, beans, broth, sugar, salt, and pepper.
Boil; reduce heat to low and simmer uncovered 1.5 hours, stirring occasionally, until thickened.
Adjust seasoning; serve hot with sour cream and cheese.