Cook fettuccine according to package directions in a large pot of boiling water. Drain.
Meanwhile, melt butter in a large skillet over medium-low heat. Add garlic and sauté until golden.
In a cup, add milk to cornstarch to create slurry and then stir into butter mixture. Add cream; stir until thicken. Add Parmesan cheese, salt, black pepper and nutmeg: stir and cook for an additional minute.
Add cooked fettuccini to the sauce, stir to coat pasta. Garnish with chives and serve immediately.
Milk and cream can be replaced with half and half, or for a thinner sauce use all milk.