Season the cut sides of the spaghetti squash with the olive oil and some salt and pepper. Place the spaghetti squash cut-side down on a large baking sheet and bake until the squash is tender and the flesh can be scraped with a fork into "spaghetti" strands, 40 to 45 minutes.
Allow to cool slightly. Using a large fork, carefully scrape the strands of spaghetti squash into a large bowl, roughly separating them as you go. While still warm, drizzle with the truffle oil, sprinkle with the Parmigiano-Reggiano and parsley and season to taste with pepper. Toss gently and serve.