Preheat an oven to 350 degrees F (175 degrees C). Coat a baking sheet with cooking spray.
Place the squash halves cut-side down onto the prepared baking sheet.
Bake in the preheated oven until the squash skin is easily pierced with a fork, 40 to 45 minutes. Remove from oven and allow to cool. Once the squash is cool enough to handle, shred squash flesh from rind using a fork; set aside in a large bowl.
Melt the butter in a skillet over medium heat; cook and stir the shallot and garlic in the hot butter until softened, 3 to 5 minutes. Stir the pumpkin puree, Greek yogurt, and Parmesan cheese with the shallot and garlic until well combined; cook until hot. Remove from heat and scrape the sauce into the bowl with the squash. Drizzle with the truffle oil; season with salt and pepper.