In a glass baking dish, arrange the squash cut-side down in about 1/2 inch of water. Cover the dish with aluminum foil. Bake for 20-30 minutes (depending on the size of the squash) or until it is tender and easily pierced with a fork. Remove from the oven and allow to cool slightly.
In a large bowl, whisk together the oil, basil, oregano, and 1/2 teaspoon Parmesan. Season the mixture with salt and pepper.
When the squash is cool enough to handle, scrape it with a fork to form strands. Add the strands to the oil mixture, and toss until combined. Sprinkle with the remaining Parmesan, and enjoy!