In a large Dutch oven or deep skillet, cook the prosciutto over medium heat until crispy. Transfer to a large slow cooker.
Season short ribs with salt and pepper generously. On the same Dutch oven or pan, heat some olive oil (about 2 tablespoons) over medium-high heat and sear all sides of the short ribs until beautifully browned. If needed, do it in batches to avoid overcrowding the pan (overcrowding will result in steaming rather than browning). Transfer the browned short ribs to a large slow cooker.
Do not wipe the Dutch oven or skillet clean. Heat about 1-2 tablespoons olive oil in same Dutch oven or skillet. Add onions and carrots, and cook for 6-8 minutes over medium-high heat until softened. Once the onions start to release moisture, scrape the brown bits (left behind from browning the short ribs) with a wooden spoon. Add garlic and mushrooms and cook until fragrant, another 1-2 minutes. Add tomato paste and stir to combine.
If using, add wine and deglaze the Dutch oven or pan. Cook until reduced.
Stir in crushed tomatoes, bay leaves, and Italian seasoning. Bring to a boil and adjust seasoning with salt and pepper as needed. Simmer for 3-5 minutes. Transfer the tomato sauce to the slow cooker along with the browned short ribs and the cooked prosciutto.
Cook on HIGH for 4 hours or on LOW for 8 hours. When the meat is ready, shred with a fork and discard bones. Return the shredded meat to slow cooker. Keep the slow cooker on the warm setting.
Cook the pappardelle or your favorite pasta according to package directions. Serve with the short rib ragu, fresh burrata, and fresh parsley. Enjoy!