Preheat the oven to 350° F. Line a baking sheet with parchment paper. Arrange the prosciutto in a single layer. Bake for 10-15 minutes or until the prosciutto is crisp. Meanwhile, melt together the butter and onions in a large Dutch oven over medium-high heat. Cook, stirring occasionally until softened, about 10 minutes. At this point, you'll want to slowly add 3/4 cup of the wine, 1/4 cup at a time, until the wine cooks into the onions. Continue to cook another 10-15 minutes until you've used the 3/4 cup of wine and the onions are deeply caramelized.Add the garlic, mushrooms, thyme, and sage. Season with salt and pepper, cook another 3-4 minutes. Add the remaining 1/2 cup wine, the broth, Worcestershire sauce, and a pinch each of salt and pepper. Increase the heat to high and bring to a boil. Add the pasta and stir frequently until the pasta is al dente and the broth has been absorbed, about 8-10 minutes. Stir in the cream and gruyere cheese. Remove from the heat.Break the burrata over the pasta and gently stir. Top with prosciutto. Eat and enjoy!