Preheat your oven to 425°F. Toss the cubed butternut squash with 2 tablespoons. of olive oil, salt, and pepper on a baking sheet. Spread into a single layer and roast in the preheated oven for 25-30 minutes, or until the squash is tender and begins to caramelize, stirring halfway through the cooking time.
While the squash is roasting, cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain, reserving 1 cup of pasta water, and set aside.
Heat the remaining 1 tablespoon of olive oil in a large skillet over medium heat. Add the sage leaves and fry until crispy, about 1-2 minutes. Remove the sage with a slotted spoon and set aside on a paper towel. In the same skillet, add the minced garlic and sauté for about 1 minute, or until fragrant but not browned. Add the roasted butternut squash to the skillet with the garlic, tossing to combine. If the mixture seems dry, add a little of the reserved pasta water to create a light sauce.
Add the cooked pasta to the skillet, tossing everything together until the pasta is well coated with the sauce. If needed, add more pasta water to achieve your desired consistency.
Crumble the fried sage leaves over the pasta and mix gently. Serve the pasta hot, garnished with grated Parmesan cheese and additional chopped sage.