Place racks in upper and lower third of oven. Preheat oven to 425ºF.
Arrange carrots and squash on separate baking sheets and lightly coat in oil. Season the carrots with cumin, coriander, turmeric, paprika, salt and pepper. Season squash with salt, pepper and a little freshly grated nutmeg. Roast carrots and squash until tender, switching the trays in the oven once, until golden at edges, about 25 minutes.
Bring a large pot of water to a boil for pasta. Add salt and under-cook pasta by a minute or two -- it will continue to cook in the oven.