Preheat oven to 375°F (190°C). Place prosciutto on a baking sheet and bake 10–12 minutes until crisp. Remove, cool, and crumble.
In a large pot or Dutch oven, heat butter and olive oil over medium heat. Add onions and cook slowly for 25–30 minutes, stirring often, until golden and caramelized.
Add garlic and thyme, cooking for 1 minute until fragrant.
Deglaze with white wine (if using), scraping up any browned bits, and let reduce slightly.
Pour in broth and bring to a boil. Add pasta and cook uncovered, stirring occasionally, until pasta is al dente and most liquid is absorbed.
Stir in cream and Gruyère cheese until sauce is creamy and smooth. Season with salt and pepper.
Serve pasta topped with crispy prosciutto crumbles and fresh parsley.