Preheat oven to 400°.
Slice each chicken breast along one side to create a pocket. Be sure not to cut the chicken breasts all the way through.
Stuff each pocket with 1 slice provolone cheese and 1-2 Tbsp. pesto. Pinch chicken breasts closed and use toothpicks to secure.
In a large skillet, heat 2 Tbsp. olive oil over medium-high heat. Place chicken in skillet, season with salt and pepper, and cook 4-5 minutes on each side. Remove from heat.
Add 3 Tbsp. butter to a large baking pan. Place in preheated oven to melt butter, then add 3 Tbsp. lemon juice and mix to combine.
Place chicken breasts in baking pan; cover with foil and bake 15 minutes or until chicken is cooked through. Remove from oven; sprinkle with shaved parmesan.
Combine remaining pesto with 2 Tbsp. olive oil; spoon over chicken breasts.
Top with halved tomatoes and fresh basil.