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 sprinkle with the sugar and salt. Stir to coat evenly.
03 - Continue cooking 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 in the minced garlic and cook for 1 minute until fragrant, being careful not to let it brown.
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 salt to taste.
06 - Add the drained pasta to the skillet with the sauce. Toss thoroughly, adding the reserved pasta water a little at a time until the sauce becomes silky and clings beautifully to every strand.
07 - Transfer to warm serving plates or bowls immediately. Finish with a generous sprinkling of chopped fresh parsley and additional grated Parmesan cheese.