Cook the pasta in a large saucepan of salted boiling water until al dente. Cook according to the packet instructions for dried pasta or for 2 minutes if using fresh pasta.
Meanwhile, melt the butter in a wide, heavy-based pan. Add the cream and bring to the boil. Reduce the heat and simmer for 1 minute until slightly thickened.
Drain the pasta thoroughly, then toss it into the pan with the cream sauce over a very low heat. Add the nutmeg, Parmesan and milk, and season with salt and pepper. Toss gently until the sauce has thickened and the pasta is well coated. Serve immediately with a scattering of grated Parmesan.