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. Reserve 1/2 cup of the starchy cooking water before draining through a colander.
02 - While the pasta cooks, melt the butter with olive oil in a large skillet set over medium heat. Add the thinly sliced onions and season with 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, deglaze with a splash of water and continue cooking.
04 - Add the minced garlic to the caramelized onions and stir for about 1 minute until fragrant and softened.
05 - Reduce the heat to low and pour in the heavy cream and whole milk, stirring gently to combine. Fold in 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 - Transfer the drained pasta into the skillet with the cream sauce. Toss thoroughly, adding small amounts of the reserved pasta water as needed until the sauce becomes silky and clings evenly to every strand.
07 - Divide among warm plates immediately. Finish each portion with a sprinkle of chopped fresh parsley and an extra shower of grated Parmesan.