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 - Combine mayonnaise, minced garlic, lemon juice, and salt in a small bowl. Mix until smooth and refrigerate until ready to use.
04 - Heat grill pan or skillet over medium-high heat. Cook chicken fillets for 4-5 minutes per side until golden and cooked through to an internal temperature of 165°F. Add cheese slices during the final minute to melt, if using.
05 - Lightly toast the split buns until golden brown and crisp.
06 - Spread garlic mayonnaise generously on both halves of each toasted bun. Layer lettuce leaves, tomato slices, and grilled chicken on the bottom bun. Close with the top bun and serve immediately.