Preheat oven to 500 degrees. Meanwhile line a baking sheet with parchment paper and set aside.
Cut each peeled and seeded squash half where the neck meets the base. Cut each quarter into 1 inch wedges and place into a bowl. Toss the squash with avocado oil, sugar, salt, and cayenne and place onto baking sheet. Make sure that the wedges are not overlapping or touching.
Roast for 10-15 minutes or until caramelized. Flip and roast the other side for another 10-15 minutes. Remove from oven, place onto a plate, and sprinkle with Parmesan.