Set a large pot of salty water to a boil. Cook the spaghetti according to package instructions. Drain and set aside.
Melt the butter in a large saucepan. Add in the garlic and cook until brown and fragrant, around 1-2 minutes. Add in the pumpkin puree, vegetable broth, nutmeg, chili powder, paprika and black pepper, and stir to combine. Mix in the coconut milk and cooked spaghetti.