Flatten the chicken by pacing it between a piece of plastic wrap or waxed paper on a cutting board. Then, using a kitchen mallet or heavy skillet, pound the chicken out to an even thickness, around ¾ of an inch thick.
Lightly coat the chicken with olive oil then season with salt, pepper, and Italian seasoning.
Preheat your grill to medium-high heat. Then cook the chicken for around 3-4 minutes per side until cooked through to an internal temperature of 165° F.
In the last minute or two of cooking top the chicken with the mozzarella cheese and close the lid to allow the cheese to melt.
Top with the chopped tomatoes, around 1 Tablespoon of pesto, and some finely grated parmesan cheese before serving.
To bake, season the chicken then bake at 375°F for around 20 minutes until they reach an internal temperature of 165°F. In the last few minutes of cooking remove the chicken from the oven and top with the cheese then return to the oven to finish cooking. Once the cheese has melted and the chicken is cooked through remove from the oven and top with the tomatoes and pesto.