01 - Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook according to package instructions until al dente. Reserve 1/2 cup of the pasta cooking water before draining.
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.
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 in the minced garlic 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 Parmesan cheese, black pepper, and nutmeg if using. Simmer for 2 to 3 minutes until the sauce thickens slightly. Season with salt to taste.
06 - Transfer the drained pasta to the skillet and toss thoroughly to coat every strand. Add the reserved pasta water a little at a time until the sauce reaches a silky, creamy consistency that clings to the noodles.
07 - Serve immediately in warm bowls, garnished with chopped fresh parsley and an extra shower of grated Parmesan.