To roast the squash: Preheat the oven to 375 degrees F.
Cut the squash in half and scrape out the seeds with a spoon.
Set the squash halves on a baking sheet, cut sides up, and sprinkle with salt and pepper. Drizzle with olive oil and sprinkle the brown sugar on top. Bake until tender abut 45 minutes.
Cook fish and sauce while squash finishes roasting: Pat fish dry and sprinkle with cumin, salt and pepper. Heat butter and oil in a sauce pan over medium heat, add the red pepper flakes, garlic and cook for 2 minutes. Add the fish and sautué, turning over once, until browned, just cooked through, 6 to 8 minutes total.
Transfer the fish to a plate and set aside. To make the sauce In the same pan heat the butter over medium heat. Add shallots, garlic, salt, pepper and thyme and cook 4 minutes, stirring occasionally. Add the mushrooms and cook for 5 minutes, or until soft, stirring occasionally.
Place the coconut milk and butternut squash in the blender and blend until smooth. Add the coconut milk-squash mixture to the pan, increase the heat to high and bring to a boil. Reduce the heat to medium low and simmer, stirring constantly with a wooden spoon, about 5 minutes.
To serve: Place one the fillets on top of the roasted squash halves, drizzle the sauce over top and sprinkle with parmesan cheese. Place in the oven for about 5 minutes or until the cheese is melted.