01 - Bring a large pot of salted water to a rolling boil. Cook the fettuccine or spaghetti according to package directions until al dente. Reserve 1/2 cup of the starchy pasta water before draining in a colander.
02 - While the pasta cooks, melt the butter with olive oil in a large skillet over medium heat. Add the thinly sliced onions and sprinkle evenly with sugar and salt to draw out moisture.
03 - Stir the onions frequently for 25 to 30 minutes, allowing them to turn a rich golden brown. If they begin to stick to the pan, add a small splash of water to deglaze and scrape up any fond.
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. 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 directly into the skillet with the cream sauce. Toss vigorously, adding reserved pasta water a tablespoon at a time until the sauce is silky, glossy, and clings to every strand.
07 - Divide among warm serving bowls immediately. Finish with a generous sprinkle of chopped fresh parsley and additional grated Parmesan at the table.