Make the butternut squash tacos: Preheat the oven to 400 degrees F. In a large bowl, toss the squash with the oil, brown sugar, cinnamon and salt. Transfer the squash to a rimmed baking sheet and roast until a little golden and cooked through, 20 to 30 minutes. Remove the squash from the oven and cool to room temperature. Transfer it to a medium bowl and combine with the beans and cilantro.
While the squash roasts, make the beef tacos: To a large skillet, add the oil and heat over medium heat. Add the onions and garlic and cook until soft, about 8 minutes. Add the mushrooms, and cook, stirring occasionally, until the liquid is cooked out, about 10 minutes. Stir in the chili powder, cumin, coriander, cayenne and cornstarch and cook, stirring often, until the mixture is creamy looking, 3 to 4 minutes. Crumble in the beef and cook, stirring occasionally, until browned, 12 to 14 minutes.
Stir in the tomato paste, and cook until the paste turns dark and dries in the pan, about 5 minutes. Add the broth and cook until the mixture is thick and creamy, 3 to 4 minutes, then season with salt and pepper.
Serve the ground beef or squash fillings in taco shells topped with tomatoes, Cheddar cheese and sour cream.