Step 1

Position two racks in the upper and lower thirds of the oven and preheat to 400 degrees.

Step 2

Wash and dry the squash. Using a sharp peeler, peel the squash in long strips. Cut the peels into 2-inch pieces, then cut the pieces into very thin slices. Using a sharp knife, cut the squash in half lengthwise. Using a spoon, scrape out the seeds and stringy pulp, transfer them to a small bowl of water, and separate the seeds from the pulp. Discard or compost the pulp, and transfer the seeds to a clean dish towel and dry them thoroughly.

Step 3

Cut the squash flesh into 1-inch cubes. In a large bowl, toss the cubes with the onion, garlic, 1 tablespoon of the oil, the smoked paprika, 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Transfer the mixture to a large, rimmed baking sheet in one layer and roast for 35 to 40 minutes, until the squash’s edges begin to brown and the flesh is soft.

Step 4

Meanwhile, in the same bowl, toss the sage leaves, squash seeds and peels with the remaining 1 tablespoon of oil, 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Transfer them to a second rimmed baking sheet in one layer and roast for 10 to 15 minutes, tossing occasionally, until lightly crisped and golden brown. Transfer to a plate to cool.

Step 5

When the squash cubes are tender, transfer the onion quarters to the bowl of a food processor. Squeeze the garlic out of its papers into the bowl and add 1/2 cup of the coconut milk. Puree until smooth. Add the remaining coconut milk, squash cubes, 3 of the roasted sage leaves and the lemon juice, and pulse a few times until thick but still chunky. Taste, and add more salt, pepper and lemon, if needed. Transfer the sauce to a large serving bowl and add the arugula.

Step 6

In a large pot of salted boiling water, cook the pasta according to the package instructions until al dente, then use tongs to transfer it directly to the serving bowl. Toss to combine. Add the remaining sage leaves, roasted peels and seeds, and serve hot.