Step 1Roast the poblano chiles: Place the chiles on a rack set over a gas stove-top burner at high heat. Roast, turning frequently, until the skin on all sides of each chile is charred, about 5 minutes. (If you have an electric or ceramic stove-top, roast the chiles in the oven using the broiler setting until charred on all sides.) Wrap each pepper in plastic wrap and set aside until the peppers are cool enough to handle, then peel the skin (the skin should stick to the plastic wrap). Rub the plastic wrap against the skin to loosen and remove it. Do not rinse the peppers to remove the skin, as rinsing will remove flavor. Stem and seed each pepper, then finely dice the chiles and set aside.
Step 2In a heavy-bottom pot, heat the oil over medium heat. Add the onion and cook, stirring frequently, until the onion is softened, 6 to 8 minutes. Stir in the diced chiles and garlic and cook until the garlic is aromatic, about 1 minute. Stir in the ground turkey and cook until the turkey is browned, 6 to 8 minutes.
Step 3Add the chili powder and cumin and cook, stirring for 2 to 3 minutes to marry the flavors. Add the ale and continue to cook, scraping any flavoring from the bottom of the pot.
Step 4Stir in the shredded turkey, crushed tomatoes and beans, along with 1 teaspoon salt, or to taste, and bring to a very gentle simmer. Cover loosely and simmer, stirring occasionally, for 30 to 40 minutes to develop the flavors. Taste and adjust the flavorings and seasonings as desired.