01 - Bring a large pot of salted water to a rolling boil. Cook fettuccine or spaghetti according to package directions until al dente. Reserve 1/2 cup of pasta cooking water before draining in a colander.
02 - While the pasta cooks, melt butter with olive oil in a large skillet over medium heat. Add the thinly sliced onions and sprinkle evenly with sugar and salt.
03 - Stir the onions frequently for 25 to 30 minutes until they turn a deep golden brown. If the onions begin to stick to the pan, add a small splash of water to deglaze and continue cooking.
04 - Stir the minced garlic into the caramelized onions and cook for 1 minute until fragrant.
05 - Reduce heat to low. Pour in the heavy cream and whole milk, stirring to combine with the onions. Add grated Parmesan cheese, black pepper, and nutmeg if using. Simmer gently for 2 to 3 minutes until the sauce thickens slightly. Season with salt to taste.
06 - Transfer the drained pasta into the skillet with the cream sauce. Toss thoroughly, adding reserved pasta water a little at a time until the sauce becomes silky and clings evenly to every strand.
07 - Serve immediately in warmed bowls, garnished with chopped fresh parsley and additional grated Parmesan.