Slice each chicken breast in half horizontally to create four evenly sized cutlets. Place the cutlets between two large sheets of parchment paper and lightly pound them to an even 1/4-inch thickness. Transfer the prepared cutlets to a gallon-size zip-top bag.

Thinly slice the green onions, reserving the dark green portions for garnish. Add the white and light green portions to a small food processor or blender along with the buttermilk and minced garlic. Blend the mixture until smooth.

If preparing the optional sauce, reserve 3 tablespoons of the blended marinade. Pour the remaining marinade into the zip-top bag with the chicken cutlets. Seal the bag securely and turn it several times to ensure all pieces are evenly coated. Refrigerate and marinate for at least 30 minutes and up to 8 hours.

Place a large cast-iron skillet over medium heat and add the oil. When the oil is hot, remove the chicken from the marinade, allowing any excess to drip off. Discard the used marinade.

Transfer the cutlets to the skillet in a single layer. Season the exposed sides with kosher salt and black pepper. Cook the chicken until the underside is golden brown, approximately 5 minutes. Carefully flip each cutlet and continue cooking for an additional 2–4 minutes, or until both sides are golden and the internal temperature reaches 165°F (74°C).

Remove the chicken from the skillet and allow it to rest on a cutting board for 5 minutes before serving.

If desired, combine the reserved marinade with the mayonnaise and season lightly with salt and pepper.

Serve the chicken cutlets whole or sliced, garnished with the reserved sliced green onion tops and the optional sauce.