01 - Bring a large pot of salted water to a rolling boil. Add the fettuccine or spaghetti and cook according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water before draining through a colander.
02 - While the pasta cooks, melt the butter with the olive oil in a large skillet set over medium heat. Add the thinly sliced onions and sprinkle evenly with the sugar and salt.
03 - Continue cooking the onions, stirring frequently, for 25 to 30 minutes until they turn a deep golden brown. If the onions begin to stick to the pan, add a splash of water to deglaze the fond and keep the cooking process moving.
04 - Stir the minced garlic into the caramelized onions and cook for about 1 minute until fragrant and softened.
05 - Reduce the heat to low. Pour in the heavy cream and whole milk, stirring gently to combine. Add the grated Parmesan cheese, black pepper, and nutmeg if using. Let the sauce simmer for 2 to 3 minutes until it thickens slightly and coats the back of a spoon. Season with additional salt to taste.
06 - Transfer the drained pasta directly into the skillet with the cream sauce. Toss thoroughly, adding small amounts of the reserved pasta water as needed to create a silky sauce that clings evenly to every strand.
07 - Serve immediately while hot. Finish each portion with a generous sprinkle of chopped fresh parsley and additional grated Parmesan cheese.