Prepare the chicken: slice each large chicken breast in half lengthwise, then place between plastic wrap and pound to about 1/4-inch thickness; season both sides with salt and pepper.
Set up a breading station with three shallow bowls: one with the all-purpose flour, one with the beaten eggs, and one with the panko.
Coat each chicken cutlet in flour, shaking off excess, then dip in the beaten eggs, and press into the panko until evenly coated.
Heat enough oil in a large skillet over medium-high heat until shimmering (about 1/4–1/2 inch deep).
Fry the breaded chicken in the hot oil for 3–4 minutes per side, or until golden brown and cooked through (internal temperature 165°F/74°C).
Transfer cooked cutlets to a paper towel-lined plate to drain briefly, then slice if desired and serve with tonkatsu sauce, garnished with sliced green onions and sesame seeds.