Bring a large pot of water to a boil for the pasta. Add 1 tbsp salt into water and add the pasta. Cook until just shy of al dente. Drain, reserving 1 cup cooking water.
Meanwhile, in a large skillet, melt butter over medium heat. Add coconut milk and bring to a simmer. Whisk in pumpkin and nutmeg. Add cheddar and parmesan and stir until melted. Season with salt.
Add pasta to the sauce and stir until coated, adding some pasta cooking water if the sauce is too thick.
Season to taste with salt and pepper, then serve immediately, topped with chives if desired.