Preheat oven to 450ºF. 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, 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.