Preheat oven to 400°F (200°C).
Toss butternut squash cubes with olive oil, salt, and pepper on a rimmed baking sheet.
Roast squash for 25 to 30 minutes, turning once, until tender and caramelized.
Bring a large pot of salted water to a boil and cook fettuccine according to package directions until al dente.
While pasta cooks, melt butter in a large skillet over medium heat.
Add sage leaves to the butter and cook until leaves are crispy and butter begins to brown and smells nutty, approximately 3 to 5 minutes.
Remove sage leaves with a slotted spoon and set aside on a paper towel-lined plate.
Drain pasta, reserving 1/2 cup of the starchy pasta water.
Add the roasted squash, cooked pasta, and nutmeg to the skillet with the brown butter.
Toss gently to coat, adding reserved pasta water 1 tablespoon at a time as needed to create a light sauce emulsion.
Divide into bowls and garnish with crispy sage leaves, grated Parmesan cheese, and toasted pine nuts.