01 - Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy cooking 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 season with the sugar and salt, tossing to coat evenly.
03 - Continue cooking the onions for 25 to 30 minutes, stirring frequently, 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 in the minced garlic and cook for about 1 minute, just until fragrant and softened.
05 - Reduce the heat to low and pour in the heavy cream and whole milk, stirring to combine. Add the Parmesan cheese, black pepper, and nutmeg if using. Simmer gently for 2 to 3 minutes until the sauce thickens slightly and coats the back of a spoon. Season with salt to taste.
06 - Add the drained pasta to the skillet and toss thoroughly to coat every strand. Add the reserved pasta water a splash at a time until the sauce reaches a silky, creamy consistency that clings to the noodles.
07 - Transfer to warm serving bowls immediately. Finish with a generous sprinkle of chopped fresh parsley and additional grated Parmesan cheese. Serve right away while hot.