1. Pick over dried beans, discarding any stones or broken beans; rinse. Place in a large saucepan, cover with cold water by 2 inches, and bring to a strong boil over high heat. Cover, and remove from heat; let stand 1 hour. Drain the beans; set aside.

2. Meanwhile, place peppers directly over the trivet of a gas-stove burner over high heat or on a grill. As they turn black, turn with tongs. (Alternatively, place peppers on a baking pan; broil in oven, turning as peppers become charred.) Transfer charred peppers to a medium bowl; cover with plastic wrap. Let peppers rest 15 minutes. Transfer to a work surface (do not rinse). Peel off blackened skin; discard. Halve peppers; remove seeds and ribs; discard. Cut pepper into 1/4-inch pieces; set aside.

3. Heat butter in a large saucepan over medium heat. Add garlic, onion, carrot, and celery. Cover; cook, stirring occasionally, until softened and slightly browned, about 15 minutes. Add cumin, coriander, paprika, and cayenne, if using; stir to combine. Stir in stock, water, beans, and half the roasted poblano peppers. Cover; cook until beans are soft, about 1 1/2 hours. Uncover; simmer gently until beans begin to fall apart, about 30 minutes more. Season with salt and pepper. Serve chili garnished with remaining poblano peppers, radish, cilantro, and yogurt cheese, if desired.