To roast the peppers, heat the oven to 425°F. Line a baking sheet with foil and place peppers on top. Roast for about 30 minutes, turning every 10 minutes, until skins are blistered and pulling away. Place in a bowl and cover to steam. When cool enough to handle, gently peel away skins. Remove stems and seeds and chop peppers.
3 to 4 poblano peppers
In a large pot, melt butter over medium heat. Add the onion, carrot, and celery with a pinch of salt and cook 5 minutes. Add the garlic and cook 1 minute more. Stir in the flour to coat the vegetables and soak up any extra butter, then mix in spices and cook 1 minute.
3 tablespoons unsalted butter, 1 medium onion, 1 cup diced carrots, 2 ribs celery, 3 cloves garlic, 2 tablespoons all-purpose flour, 1 to 2 teaspoons chili powder, 1 teaspoon fine sea salt, 1 teaspoon ground cumin, 1/4 teaspoon ground black pepper
Stir in a small amount of broth to deglaze the pan and scrape up any stuck bits. Add the chicken, corn, poblano peppers, and remaining broth and stir well.