Preheat oven to 425F.
Place butternut squash cut side up on a baking sheet and drizzle with about 2 tablespoons EVOO and some salt and pepper. Roast squash in oven until tender, about 45 minutes. When they've finished roasting, turn off the oven and turn on the broiler.
While the squash is in the oven, place a medium saucepan over medium-high heat with 3 turns of the pan of EVOO, about 3 tablespoons. Add the mushrooms and brown 5 minutes alone, then add onion, garlic, peppers and zucchini to the pan, season with salt and pepper and cook until the veggies are tender, about 8-10 minutes more. Puree softened ancho chili peppers in food processor or blender with vegetable stock.
Add the spices, corn, black beans and tomato paste to the pan and cook until heated through, 1-2 minutes. Add the beer to the pan, stir then add ancho stock then simmer over low heat until ready to serve.
Scoop the finished chili over the butternut squash halves and sprinkle with the cheese. Place the squash under the broiler to melt the cheese then serve.