Caramelize the onions: Melt butter and olive oil in a large pot or Dutch oven over medium heat. Add the sliced onions, salt, and pepper. Cook, stirring occasionally, for 20-30 minutes, or until deeply caramelized and golden brown. Reduce heat if they brown too quickly.

Deglaze (optional): If using white wine, add it to the pot and scrape up any browned bits from the bottom. Let it simmer for 1-2 minutes until slightly reduced.

Simmer the broth: Pour in the beef broth, heavy cream, thyme, and sugar. Bring to a simmer, then reduce heat to low and simmer gently for 15 minutes.

Cook the pasta: While the sauce simmers, cook the pasta according to package directions until al dente. Reserve about 1/2 cup of the pasta cooking water before draining.

Combine: Add the cooked pasta to the onion sauce. Stir in the Parmesan cheese and a little reserved pasta water if needed to thin the sauce.

Garnish and serve: Serve immediately, garnished with fresh parsley and extra Parmesan cheese, if desired.