In a dry medium-sized skillet, toast the dried chiles over medium heat until warm and fragrant, turning occasionally, for about 2 minutes. Transfer to a cutting board and let cool.
Meanwhile, preheat the oven to 350 F and line a roasting pan with parchment paper. Prepare the butternut squash (peel, deseed, and cube the raw squash) and place the cubes on the prepared tray. Chop the onion into eighths, trim the ends off the garlic cloves, and place on the tray with the squash. Drizzle everything with olive oil, sprinkle with salt and a little cracked pepper, than roast until softened, rotating the pan and flipping the vegetables over halfway through, for about 30-50 minutes total. Squeeze the roasted garlic cloves out of their skin and discard the skins.
While the squash and alliums roast, soak the toasted chiles. Using gloves if you're heat-sensitive, rip off the stems and carefully dump out the seeds. Put the deseeded chiles in a medium saucepan, pour the chicken broth over top, then bring to a boil over high heat. Remove the pan from the heat and let the chiles stand in the liquid until very soft, about 30 minutes.
Once the squash is roasted and the chiles are softened, work in batches to transfer the squash, onions, garlic, chiles, and chicken broth to a blender and puree until smooth.
Heat a large, heavy-bottoms soup pot or Dutch oven over medium-high heat. Add a drizzle of olive oil to the pot, then the ground turkey meat and the ½ teaspoon salt and cook the ground turkey, breaking it up into bite-sized chunks, until it turns opaque throughout and starts to brown in a few spots. Add the tomato paste and cumin, stir in, and continue cooking until the cumin is fragrant, about 1-2 minutes. Add the cocoa powder and brown ale, stir well, and bring to a boil. Add the chile-squash puree and apple cider, bring back to a boil, then reduce the heat to medium-low. Simmer until the chili thickens and is very flavorful.
This chili is good immediately, however, it's actually best the day(s) after it is made so the flavors really have time to settle. Stir in baby spinach or spiralized zucchini to wilt and serve, with avocado chunks, cheese, chopped cilantro, chips, and any other accompaniments you want on the side.
Once made, this chili will keep in the refrigerator for about 4 days or in the freezer for 1-2 months.