Ingredients
2 pounds bone-in, skin-on chicken thighs (4 to 5)
Kosher salt and freshly ground pepper
1 stick (8 tablespoons) cold unsalted butter
2 cups chopped poblano chiles (from 2 large)
1 onion, diced (1 1/2 cups)
3 carrots, diced (1 1/4 cups)
1 stalk celery, diced (1/2 cup)
8 ounces white potato, peeled if desired and cut into 1/2-inch dice (1 1/2 cups)
1/2 teaspoon dried thyme
1 1/4 teaspoons chili powder
1 1/3 cups plus 1/4 cup unbleached all-purpose flour
1 cup frozen corn
6 tablespoons chopped cilantro, plus more for serving
1/3 cup finely ground cornmeal
2 teaspoons baking powder
3/4 cup whole milk
Lemon wedges, for serving
Preparation
Combine chicken, 2 teaspoons salt, and 4 cups water in a medium saucepan. Bring to a boil, then reduce heat to medium-low and simmer, partially covered, until chicken is cooked, about 20 minutes. Transfer chicken to a plate; let cool 10 minutes. Discard skin and bones; shred meat into bite-size pieces (you should have 3 cups). Strain broth (you should have 4 cups; if not, add more water).
Melt 4 tablespoons butter in a large pot over medium-high heat. Saute chiles 5 minutes. Add onion, carrots, celery, potato, thyme, and chili powder. Cook, stirring, until onion is translucent, 3 to 4 minutes. Sprinkle with 1/4 cup flour; cook 30 seconds. Gradually stir in broth. Bring to a boil, then reduce heat to medium and simmer 2 minutes. Stir in chicken, corn, and 3 tablespoons cilantro. Season with salt and pepper.
Meanwhile, whisk together remaining 1 1/3 cups flour, cornmeal, 3 tablespoons cilantro, baking powder, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper. Cut in remaining 4 tablespoons butter. Stir in milk until dough holds together. Drop 8 heaping spoonfuls of dough on top of chicken mixture. Cover and simmer until dumplings are cooked through, about 12 minutes. Serve with more chopped cilantro and lemon wedges.