Broil poblano peppers, turning, until blackened, 15 minutes. Place in bag; close; let stand 15 minutes. Core, seed, peel and coarsely chop.
Puree roasted peppers, tomatillos, onion, cilantro, chilies and jalapeno into processor or blender.
Heat oil in Dutch oven over medium-high heat. Working in batches, sauté pork until browned, about 10 minutes; transfer to plate.
Add onion and garlic to pot; cook until tender, 8 minutes. Stir in cumin, sugar and salt; cook 1 minute. Return meat to pot. Stir in roasted pepper mixture and broth. Cover; cook at hard simmer until meat is tender, 1 hour. Uncover last 15 minutes if chili needs thickening. Garnish with cilantro sprigs.