01 - Butterfly the chicken breasts horizontally to create four thin fillets of even thickness.
02 - Whisk together olive oil, minced garlic, oregano, salt, and pepper in a bowl. Add chicken fillets and turn to coat thoroughly. Let marinate at room temperature for 10 minutes.
03 - While chicken marinates, combine mayonnaise, minced garlic, lemon juice, and salt in a small bowl. Mix until smooth and refrigerate until ready to use.
04 - Heat a grill pan or skillet over medium-high heat. Cook chicken fillets for 4 to 5 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Add cheese slices during the final minute of cooking if desired.
05 - Lightly toast the cut sides of sandwich buns until golden and crisp.
06 - Spread garlic mayonnaise generously on both halves of each toasted bun. Layer lettuce leaves, tomato slices, and grilled chicken on bottom buns. Cover with top bun and serve immediately.