Set your oven to 400°F (200°C) and lay parchment paper on a large baking sheet.
First, slice off the stem end of the acorn squash, removing about 1/4 to 1/2 inch. Stand the squash upright on a wooden cutting board, cut side down, ensuring it's stable. Then halve it vertically with a sharp knife. Scoop out seeds with a spoon and discard. Arrange the halves flesh-side down on the prepared sheet. Roast for 50 minutes to 1 hour, until the squash is completely tender when pierced with a fork. Allow it to cool briefly before extracting the flesh.
While the squash roasts, place a large skillet over medium-low heat. Add the hazelnuts and toast for 2-3 minutes, until golden and aromatic. Transfer to a plate and set aside.
Put the cooked squash flesh into a high-powered blender or food processor. Add the milk, maple syrup, cinnamon, and nutmeg. Blend until silky, adding more milk as needed to achieve the desired consistency. Set aside.
Using the same skillet, melt the butter over medium heat. Stir constantly as it melts, crackles, and then foams. After a few minutes, the butter will turn a rich amber color on the bottom, typically right when it foams. Continue whisking, then remove from heat as soon as it browns and smells nutty. Keep the butter in the pan but off the heat to cool slightly while you cook the pasta.
Boil the spaghetti per package instructions. Drain and transfer to the skillet with the brown butter, tossing to coat evenly. Immediately pour in the acorn squash sauce and garlic powder, stirring until creamy. Season generously with salt and pepper, adjusting to taste. Finish with sage, toasted hazelnuts, and shaved parmesan, mixing in if preferred.