1. Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper for easy cleanup.

2. Toss the cubed butternut squash with olive oil, 0.5 teaspoon of the salt, and 0.25 teaspoon of the black pepper. Spread the squash in an even layer on the baking sheet.

3. Roast the butternut squash for 20–25 minutes, tossing halfway through, until the edges are caramelized and the centers are tender when pierced with a fork.

4. While the squash roasts, bring a large pot of salted water to a boil. Add the rigatoni and cook according to package directions until just al dente. Reserve about 1 cup of the pasta water, then drain the pasta.

5. In a large skillet or wide saucepan, melt the butter over medium heat. Add the sage leaves and cook, stirring often, as the butter foams and then begins to turn golden brown and smell nutty, 3–5 minutes. Remove a few crisp sage leaves and set aside for garnish.

6. Reduce the heat slightly and stir in the garlic and crushed red pepper flakes. Cook for 30–60 seconds, just until the garlic is fragrant and lightly golden.

7. If using, pour in the heavy cream and whisk to combine with the brown butter. Add about 0.25 cup of the reserved pasta water and stir to create a glossy sauce. Season with the remaining 0.5 teaspoon salt and 0.25 teaspoon black pepper.

8. Add the drained pasta to the skillet and gently fold to coat it in the brown butter sage sauce. Tip in the roasted butternut squash and toss carefully so the cubes stay mostly intact, adding more pasta water as needed to loosen the sauce.

9. Turn off the heat and stir in the grated Parmesan until it melts and clings to the pasta. Add the lemon juice, taste, and adjust seasoning with extra salt, pepper, or red pepper flakes if desired.

10. Serve the pasta immediately, topped with the reserved crispy sage leaves and an extra sprinkle of Parmesan on each bowl.