In a large pot or deep skillet, melt 2 tablespoons of butter and 2 tablespoons of olive oil over medium heat. Add 3 medium thinly sliced onions, ½ teaspoon of salt, ½ teaspoon of pepper, and 1 teaspoon of sugar. Cook slowly for 20 to 25 minutes, stirring frequently until the onions turn deeply caramelized and golden brown.

Stir in 1 tablespoon of minced garlic into the caramelized onions and cook for an additional minute. Then pour in 1 tablespoon of balsamic vinegar and sprinkle in 1 teaspoon of thyme. Mix everything well.

Next, add 12 ounces of dry pasta into the pot along with 4 cups of beef broth and 1 cup of water. Bring to a boil while stirring occasionally, then reduce heat to simmer for 12 to 15 minutes until the pasta is tender.

Once the pasta is cooked, stir in ½ cup of heavy cream, 1 cup of shredded Gruyère cheese, and ½ cup of grated Parmesan cheese. Allow the cheeses to melt into the sauce, stirring gently.

Serve in bowls, garnishing each with fresh parsley and additional Parmesan cheese if desired.