Preheat the oven to 350 degrees F (175 degrees C).

Coat inside of squash with 1 tablespoon olive oil. Place squash cut-side down on a baking sheet.

Bake in the preheated oven until squash is tender, about 30 minutes. Cool squash for 10 minutes.

Shred inside of squash with a fork and transfer to a bowl. Add remaining olive oil, parsley, red pepper flakes, salt, and pepper to shredded squash and toss to coat.