01 - Bring a large pot of generously salted water to a rolling boil. Add the fettuccine or spaghetti and cook according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy pasta water. Drain the pasta and set aside.
02 - While the pasta cooks, melt the butter with the olive oil in a large skillet over medium heat. Add the thinly sliced onions and sprinkle evenly with the sugar and salt to encourage browning.
03 - Cook the onions, stirring frequently, for 25 to 30 minutes until they turn a rich golden brown and become deeply caramelized. If the onions begin to stick to the pan, add a splash of water to deglaze and continue cooking.
04 - Stir the minced garlic into the caramelized onions and cook for 1 minute until fragrant, being careful not to let it brown.
05 - Reduce the heat to low and pour in the heavy cream and whole milk, stirring gently to combine. Add the grated Parmesan cheese, black pepper, and nutmeg if using. Simmer for 2 to 3 minutes, allowing the sauce to thicken slightly. Taste and adjust the salt as needed.
06 - Add the drained pasta directly to the skillet with the cream sauce. Toss vigorously to coat every strand, adding small splashes of the reserved pasta water as needed until the sauce becomes silky and clings to the noodles.
07 - Transfer to warm serving bowls or plates immediately. Finish with a generous sprinkle of chopped fresh parsley and additional grated Parmesan to taste.