Step-1In a small bowl, combine oil, half the lemon juice, 1 teaspoon salt, 1/4 teaspoon pepper, and Italian seasoning (or oregano) and whisk to combine. Transfer to a large re-sealable bag along with chicken; seal and refrigerate for 30 minutes.
Heat grill over medium-high then add chicken, discarding excess marinade. Grill until charred and cooked to an internal temperature of 165°, about 5 to 7 minutes per side.
Meanwhile, combine tomatoes, garlic, basil, and remaining lemon juice, and season with salt and pepper. While chicken is still on grill, top each breast with 1 slice mozzarella and cover until cheese is melted, 2 to 3 minutes. Top chicken with tomato mixture.
Garnish with Parmesan and serve