Make vinaigrette: Place garlic, basil, and vinegar in a blender.

With the motor running, slowing drizzle in 1/3 cup plus 2 tablespoons oil until fully incorporated.

Season with salt and pepper and set aside.

Brush 1 tablespoon oil over each chicken breast and season with salt and pepper.

Place a grill pan over medium-high heat and brush with remaining tablespoon oil.

Sear each breast 2 on each side.

Lower heat to medium, cover, and continue to cook until chicken has cooked through, 8 to 10.

Transfer chicken to a cutting board and let rest, 5, then slice chicken on a bias into thin, long strips.

Add romaine into a bowl and top with mozzarella balls, halved cherry tomatoes, and chicken strips.

Drizzle with vinaigrette and garnish with fresh basil and Parmesan.