Toss the cabbage, carrot, rice vinegar, sesame oil, and salt in a medium bowl. Set aside while you prepare the tofu (the slaw will soften slightly as it sits).
Slice each pressed tofu block crosswise into 4 equal pieces, about ¾-inch thick (12 pieces total). Pat each piece dry with paper towels. Season all pieces on both sides with the salt and pepper.
Arrange three shallow dishes in a row:Dish 1: FlourDish 2: Soy milk whisked with cornstarch until smoothDish 3: Panko mixed with garlic powder, onion powder, salt, and pepper
Working with one piece at a time: coat in flour, shaking off excess. Dip in the soy milk mixture, letting excess drip off. Press firmly into the seasoned panko, coating both sides and edges thoroughly. Press the panko onto the tofu to help it adhere. Set aside on a sheet pan and repeat with remaining pieces.
Pour oil to a depth of ¼ inch in a large skillet and heat over medium heat until it reaches 350°F on an instant-read thermometer, or until a pinch of panko sizzles immediately when dropped in.I use an instant-read thermometer but you can test with a pinch of panko — it should sizzle immediately but not brown instantly.
Carefully add 3-4 breaded tofu pieces to the hot oil (don't overcrowd). Fry for 3-4 minutes per side, until deep golden brown and crispy. Transfer to a paper towel-lined plate. Repeat with remaining pieces in 3-4 batches, letting oil return to temperature between batches.
Divide rice among 4 bowls. Top each with slaw and 3 pieces of tofu katsu. Drizzle with tonkatsu sauce, sprinkle with green onions, and serve with a lemon wedge.
Notes
Press tofu 15–30 minutes (or overnight) to remove excess moisture. This is my favorite tofu press [affiliate]. Even after pressing, surface moisture affects how well the flour adheres. So make sure to pat dry!
Too cool and the coating absorbs oil and turns greasy. Too hot and it burns before heating through. Use a thermometer, or test with a pinch of panko—it should sizzle immediately but not brown instantly.
Hold finished pieces in a 200°F oven while frying remaining batches.
Overcrowding drops the oil temperature and results in soggy, uneven coating.
To make a quick tonkatsu sauce at home, whisk together 3 tablespoons ketchup, 2 tablespoons vegan Worcestershire sauce, 1 tablespoon low-sodium soy sauce, and 1 teaspoon granulated sugar.
If using an air fryer, spray the breaded tofu with oil, then air fry at 400°F for 12-14 minutes, flipping halfway through. Less crispy but much less oil.