Heat the oven and prep the squash. Set the oven to 425°F (220°C). Toss squash cubes with olive oil, salt, and pepper on a sheet pan. Spread in a single layer.

Roast until caramelized. Bake for 20–25 minutes, flipping once, until the edges are golden and the centers are tender but not mushy. Set aside.

Boil the pasta. Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente. Reserve 3/4 cup of the starchy cooking water, then drain.

Brown the butter. In a large skillet over medium heat, melt the butter. Add sage leaves and cook, stirring, until the butter foams and turns golden with brown specks and the sage crisps, about 3–4 minutes. Adjust heat as needed to prevent burning.

Add garlic and optional heat. Stir in the sliced garlic and a pinch of red pepper flakes. Cook 30–45 seconds until fragrant.

Build the sauce. Add 1/2 cup reserved pasta water to the skillet to stop the butter from getting too dark. Simmer 30 seconds, scraping up any browned bits.

Toss it all together. Add the pasta and roasted squash to the skillet. Toss gently over low heat. Sprinkle in the Parmesan and a small squeeze of lemon juice, tossing until glossy. Add more pasta water as needed to loosen and coat.

Finish and season. Taste and adjust salt and pepper. Add lemon zest for brightness. If using, fold in a handful of baby spinach to wilt slightly.

Serve. Plate with extra Parmesan and a few crispy sage leaves on top. Add toasted nuts if you like crunch.