Place racks in upper and lower third of oven. Preheat oven to 425F.
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.
Melt butter in a saucepot over medium heat. Stir in flour and cook a minute or two. Add shallots and garlic; season with mustard, salt and pepper and stir for a minute or two. Add Worcestershire then whisk in milk, bring sauce to a bubble then thicken to coat spoon.
Place half the roasted squash and carrots into food processor with chicken stock and pure. Whisk pure into milk sauce.
Stir 2 1/2 cups of cheese into sauce; combine with pasta and half the remaining carrots and squash. Transfer to a casserole dish and top with the rest of the roast carrots and squash and cheese.
Brown casserole in the hot oven or cool it and store for a make-ahead meal. If storing, bring the casserole to room temperature before baking at 375F until brown and bubbly.