Preheat the oven to 400F. Line a baking sheet with aluminum foil, and lightly grease with nonstick cooking spray or with olive oil. If you have a second baking sheet, set that up as well. It may be easier to bake two batches at the same time on different racks.
Slice the butternut squash in half, and remove the seeds from the center cavity. Peel the skin from the butternut squash if desired.
Cut the butternut squash into ¼ inch strips. Place about two cups (about half) of the butternut squash into a plastic bag, and add one tablespoon of the cornstarch. Shake the bag until the butternut squash is evenly coated with a light layer of cornstarch.
Place the butternut squash onto the baking sheet, and brush olive oil to cover all surfaces of the butternut squash. This will help the fries become crispier.
Repeat with the other half, and place on the second baking sheet. Or wait until the first batch is done to bake the second batch.
Bake one or both batches at 400F for about 15 minutes, then turn over the fries, and bake for another 15 minutes.
Once the fries have become crispy, remove the baking sheet from the oven and allow the fries to cool for a few minutes.
Toss the butternut squash fries with a little bit of salt and finely chopped parsley.