Preheat oven to 400F
Use a sharp knife to create a pocket in each of the chicken breasts.
Fill the pocket with 2 tbsp of mozzarella
Add 1½ tbsp of butter and 2 tbsp of olive oil to a 11 inch skillet. Raise the temperature to medium-high heat. Once the butter begins to foam, add the chicken, seam side down. Cook for about 2 minutes on each side or until golden brown.
Remove chicken, lower the temperature to medium, and add tomatoes + remaining 1 tbsp of olive oil. Cook for 3 minutes, then use the back of a spatula to burst the tomatoes.
Add the garlic and the Calabrian chili pepper. Mix well and cook for 2 more minutes.
Add chicken stock and raise the temperature to medium-high heat. Once the liquid is boiling, add the orzo and cook for 2 more minutes (stir occasionally to make sure the orzo does not stick), then turn off the heat.
Add back the chicken seam side up. Top each piece of chicken with ½ a piece of prosciutto.
Place the entire pan onto the middle rack of the oven and let it cook for 20 minutes or until the chicken has an internal temp of 165F.
Top with basil pesto and serve warm.