Preheat oven to 375F. Setup a breading station with three bowls. In the first, place flour, garlic, kosher salt, and black pepper, then stir to combine. In the second, place whisked eggs. In the third dish, mix together panko breadcrumbs, grated parmesan, and sliced basil.
Use the flat side of a meat tenderizer to pound out each chicken breast to about ¾" thickness. I like to place the chicken on a piece of parchment paper, then fold the excess parchment over on top of the chicken. This helps to make sure I don't destroy each chicken breast with the tenderizer.
Pat chicken breasts dry with a paper towel, then dredge each fully in the flour. Shake off any excess, then transfer to coat in eggs. Finally, move the chicken to the last bowl and coat evenly on all sides with panko and parmesan mixture. Place on a wire rack until ready to cook. Repeat with remaining chicken breasts.
Heat a large skillet over medium-high heat, then add butter and olive oil. When butter begins to sizzle, about 1-2 minutes later, add breaded chicken and cook undisturbed, 3-4 minutes. Carefully flip each piece of chicken over -- and check whether your pan is dry! If so, add another couple tablespoons of olive oil, otherwise the breadcrumbs will burn. Cook 3-4 minutes more. Remove chicken from pan when golden brown on both sides.
Turn the heat off on your skillet, then carefully pour in store-bought or homemade marinara sauce. Add 4 basil leaves, then return chicken to the pan. Top each chicken breast with fresh mozzarella, covering as much of the chicken as possible. Cook in preheated oven for 10 minutes, or until the internal temperature of chicken is 165F. Place chicken under the broiler with high heat for about 2 minutes, just until the fresh mozzarella is golden brown and bubbling. Garnish with additional fresh basil as desired, then serve immediately.