Place poblano and Anaheim peppers directly over a gas flame or under the broiler, turning frequently until the skin is completely blackened, about 10 minutes. Place in a bowl, cover with plastic wrap, and let steam for 10 minutes.
Peel the charred skin from the peppers, remove seeds and stems, then dice the peppers and set aside.
Heat olive oil in a large pot over medium-high heat and brown the ground beef, breaking it up with a spoon, about 8 minutes. Drain excess fat.
Add onion to the pot and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Stir in chili powder, cumin, and coriander, cooking for 1 minute until fragrant.
Add the roasted diced peppers, crushed tomatoes, black beans, beef broth, brown sugar, salt, and pepper. Stir well to combine.
Bring to a boil, then reduce heat to low and simmer uncovered for 1.5 hours, stirring occasionally, until the chili has thickened.
Adjust seasoning to taste and serve hot with sour cream and shredded cheese.