01 - Heat unsalted butter and olive oil in a large skillet over medium-low heat. Add sliced yellow onions, salt, pepper, and sugar. Cook, stirring frequently, for 20 to 25 minutes until onions are deeply caramelized.
02 - Add minced garlic and thyme to the onions, stirring for 1 minute until fragrant.
03 - Pour in dry white wine and simmer for 2 to 3 minutes, allowing the liquid to reduce by half.
04 - Incorporate beef or vegetable broth. Bring to a gentle simmer and cook for 5 minutes so flavors meld.
05 - Boil fettuccine or tagliatelle in salted water according to package directions until al dente. Drain, reserving 1/2 cup of pasta water.
06 - Stir heavy cream into the onion mixture and simmer for 2 minutes. Reduce heat, add Gruyère and Parmesan cheeses, stirring constantly until fully melted and velvety.
07 - Add the cooked pasta to the creamy onion sauce, using reserved pasta water as needed for desired consistency. Toss gently so pasta is evenly coated.
08 - In a dry skillet over medium heat, cook prosciutto slices for 1 to 2 minutes per side until golden and crisp. Break into shards once cooled.
09 - Serve pasta in bowls, topped with crispy prosciutto shards, fresh chopped parsley, and extra Parmesan as desired.