Place chicken breasts between plastic wrap and pound to even ¾-inch thickness. Season both sides with salt and pepper.
Set up breading station with three shallow dishes: flour in first, beaten eggs in second, and panko breadcrumbs in third.
Heat oil in a heavy-bottomed pot or deep skillet to 340-350°F. Use a thermometer to monitor temperature.
Dredge each chicken breast in flour, shaking off excess. Dip in beaten eggs, letting excess drip off. Coat thoroughly in panko, pressing gently to adhere.
Let breaded chicken rest on a wire rack for 10 minutes to set the coating.
Carefully lower chicken into hot oil, cooking 2 pieces at a time to avoid overcrowding. Fry for 3-4 minutes per side until golden brown and internal temperature reaches 165°F.
Transfer to a wire rack set over paper towels to drain. Let rest 2-3 minutes before slicing.
Slice katsu crosswise into strips and serve immediately over rice with shredded cabbage and tonkatsu sauce.
Notes
Storage tip: Store breaded uncooked cutlets in refrigerator up to 4 hours or freeze up to 3 months. Cooked katsu keeps 3 days refrigerated; reheat in 375°F oven to restore crispiness.