Preheat the oven to 450 degrees . Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 cup of the pasta cooking water.
While the pasta is working, on a baking sheet, drizzle the squash with EVOO and season with salt, pepper and grated nutmeg. Roast until tender and charred at the edges, about 18 minutes.
Meanwhile, using a food processor, pulse 1/3 cup EVOO, the herbs, cheese, pepitas, chiles, garlic and lime juice. Season with salt and pepper.
Add the pesto, reserved pasta cooking water and squash to the drained pasta. Toss gently and serve.