In a large Dutch oven or heavy pot (at least 7 quarts), toast chiles over medium heat, turning occasionally with tongs, until warm, fragrant and pliable, about 2 minutes. Let cool for a minute.
Rip stems off the chiles and remove seeds and membranes. Rip into pieces taking care to remove all seeds. Place chiles in a medium pot and add broth. Bring to a boil over high heat. Remove pot from heat and let stand until chiles are very soft, about 30 minutes. Transfer chiles and broth to a blender, Vitamix or food processor and purée until smooth. Set aside. (See Notes.)
While chiles are softening, chop onion and slice garlic. In the same Dutch oven or heavy pot, heat olive oil over medium heat. Add onion and garlic. Season generously with Kosher salt. Cook, stirring occasionally, until onion is soft, about 8 to 10 minutes.
Increase heat to medium-high and add ground turkey. Cook, breaking up with back of wooden spoon, until it’s cooked through and a bit browned, about 10 minutes.
Stir in tomato paste, cumin and cocoa powder. Cook until fragrant, about 1 to 2 minutes.
Stir in butternut squash and pumpkin ale, and bring to a boil.
Stir in reserved chile purée, apple cider or apple juice, black beans and pinto beans and bring to a boil.
Reduce heat to medium-low and simmer until chili is thick and flavorful, about 60 minutes.
Season with salt. Serve warm with garnishes.
Notes
* I used ancho chiles and it was just the right flavor without too much spice. You can also use any mixture of guajillo, pasilla or New Mexico. Chile purée can be made a day ahead and refrigerated until ready to use. * I bought already cubed butternut squash at the grocery store. I cut it into smaller pieces. * Chili can be refrigerated for up to 4 days or frozen for up to 3 months. Reheat on top of the stove or in a slow cooker.