Place the gnocchi on a microwave safe plate lined with a paper towel. Microwave the gnocchi for about four minutes on high. I would do one bag at a time.
Once thawed, pat the gnocchi dry with a paper towel to get rid of any moisture.
Preheat a skillet to medium heat and add olive oil. In batches sauté the gnocchi until crispy about two to three minutes per side adding more olive oil as needed. Just be sure to not over cook because they will become rubbery! Place the cooked gnocchi in a large bowl.
Preheat your oven to 425 degrees. Place the prosciutto slices on the baking sheet. Cook the prosciutto for about 5 minutes or until crispy. Remove and set aside.
Meanwhile, in a large non-stick skillet preheated to medium heat, melt the butter. Using a slotted spoon, add cooked gnocchi into melted butter. Season with several cranks of black pepper. Next, add the Parmesan and Pecorino and toss until melted and pepper is fragrant, about 2 minutes. Pour in the chicken stock, a couple tablespoons at a time to help sauce come together, as needed.
Serve the gnocchi on a plate with more Parmesan, crispy prosciutto, and black pepper.