1. Mix together butter, lemon juice, and 4 Tbsp. parsley until completely blended.
2. Shape into a log and wrap with plastic film. Freeze until firm, and slice into 12 slices.
3. Butterfly chicken breasts, cutting from the outside edge to the thicker center edge. Season inside and out with salt and pepper.
4. Place one slice mozzarella into each breast. Top mozzarella with 3/4 oz. chopped ham, 1/4 tsp. garlic, 1/4 tsp. tarragon, and 1/4 tsp. parsley.
5. Fold chicken over filling and secure edges with toothpicks.
6. Grill chicken breasts until golden brown and cooked through, about 8 minutes.
7. Top each chicken breast with 1 slice of compound butter, and slice into 6 pieces before serving.