Preheat the oven to 400 degrees F (200 degrees C).
Peel butternut squash using a vegetable peeler. Cut the bottom round end off and reserve for later use. Make noodles using the thickest blade of a sturdy spiralizer.
Place butternut squash noodles in a large bowl. Add olive oil, salt, pepper, and crushed red pepper flakes. Toss until evenly combined. Divide noodles between 2 large baking sheets.
Roast in the preheated oven for 8 minutes. Flip noodles and roast for 4 minutes more.
Transfer noodles to a serving dish and garnish with Parmesan cheese and parsley.