Preheat oven to 400°F (200°C). Line a large rimmed baking sheet with parchment paper.

Toss butternut squash cubes, chopped shallot, and smashed garlic cloves with olive oil, salt, and pepper. Spread into a single layer and roast for 22 to 25 minutes until the squash is fork-tender with golden caramelized edges.

Transfer warm roasted squash, shallot, and garlic into a high-speed blender. Pour in the broth and heavy cream. Blend on high for 60 to 90 seconds until completely silky, glossy, and lump-free.

Bring a large pot of generously salted water to a rolling boil. Cook fettuccine until 1 minute shy of al dente (about 9 minutes). Before draining, ladle out 1 cup of starchy pasta water; set aside.

While pasta boils, melt butter in a wide, deep skillet over medium heat. Add the whole fresh sage leaves in a single layer. Fry for 2 minutes until sage turns crisp and butter turns golden with fragrant nutty brown flecks. Use a fork to transfer fried sage to a paper towel-lined plate.

Pour the blended butternut squash puree directly into the skillet with the browned butter. Stir over medium-low heat. Add freshly grated nutmeg and grated Parmigiano-Reggiano, stirring until cheese melts smoothly into the sauce.

Add the drained fettuccine directly into the sauce. Splash in ¼ to ½ cup of reserved starchy pasta water, tossing vigorously with tongs for 2 minutes until the velvety sauce clings luxuriously to every pasta ribbon.

Twirl onto warm plates. Top with crispy fried sage leaves, shaved parmesan curls, toasted pine nuts, and freshly cracked black pepper. Serve immediately.