Place the chicken breasts between two sheets of plastic wrap and pound them to about 1/2 inch thick using a meat mallet or rolling pin.
Set up a breading station: In one shallow dish, place the flour. In a second dish, beat the eggs. In a third dish, combine panko breadcrumbs, salt, pepper, garlic powder, and onion powder.
Dredge each chicken breast in the flour, shaking off the excess. Dip into the beaten eggs, allowing any excess to drip off, then coat thoroughly with the panko mixture, pressing gently to adhere.
In a large skillet, heat about 1/4 inch of vegetable oil over medium-high heat until shimmering. Carefully add the breaded chicken breasts to the skillet, cooking for about 4-5 minutes on each side or until golden brown and cooked through (internal temperature should reach 165°F).
Transfer the cooked chicken to a paper towel-lined plate to drain excess oil. Let it rest for a few minutes before slicing.
Serve the chicken katsu with tonkatsu sauce drizzled on top or on the side, along with shredded cabbage if desired.