Place tomatoes in a small bowl; add 1 tablespoon oil, shallot, basil, vinegar, garlic, ¼ teaspoon pepper and ⅛ teaspoon salt. Toss to combine; set aside.
Pat chicken dry using paper towels; sprinkle with the remaining ½ teaspoon pepper and ⅛ teaspoon salt.
Heat the remaining 3 tablespoons oil in a large skillet over high heat. Add the chicken; cook, undisturbed, until golden brown on the bottom, about 3 minutes.
Flip the cutlets and top each with a cheese slice. Cover the pan with a lid or baking sheet; cook until the cheese is melted and a thermometer inserted into the thickest part of the chicken registers 165°F, about 1 minute, 30 seconds.
Transfer the chicken to individual plates or a platter; top with the tomato mixture and drizzle with balsamic glaze. Garnish with basil leaves, if desired.
