Place chicken breasts between plastic wrap and pound to ½-inch thickness. Season both sides with salt and pepper.
Set up three shallow bowls: flour in the first, beaten eggs in the second, and panko breadcrumbs in the third.
Dredge each chicken cutlet in flour, shaking off excess, then dip in beaten eggs, and finally coat thoroughly with panko, pressing gently to adhere.
Heat oil in a large skillet over medium-high heat to 340°F. If you don't have a thermometer, test with a pinch of panko - it should sizzle immediately.
Carefully place breaded cutlets in hot oil and cook for 3-4 minutes per side until golden brown and internal temperature reaches 165°F.
Transfer to a paper towel-lined plate to drain briefly, then slice into strips.
Serve immediately over rice with shredded cabbage and katsu sauce.
Notes
Storage tip: Breaded uncooked cutlets can be refrigerated up to 3 days or frozen up to 3 months. Cooked katsu keeps in fridge for 4 days - reheat in 350°F oven for best results.