Press the tofu for at least 10 minutes to drain excess liquid, then slice into thick slabs. Rub the first portion of salt onto both sides of the tofu.

Whisk the flour, cornstarch, baking powder, the remaining salt, and water in a medium bowl until the batter is smooth. Spread the bread crumbs onto a shallow plate or tray nearby.

Dip each tofu slab into the batter, letting any excess drip off, then press into the bread crumbs until fully and evenly coated.

Fill a large skillet with enough oil to reach halfway up the sides of the tofu and heat over high heat until the oil shimmers. Carefully place the tofu in the pan—it should sizzle immediately—ensuring the pieces do not touch.

Fry for 4 to 5 minutes, flipping halfway through, until the exterior is deeply golden brown and crisp. Transfer the slabs to a wire rack or paper towel-lined plate to drain; let them rest for a few minutes so the crust sets.

Whisk the ketchup, soy sauce, vinegar, and sugar in a small bowl until the sugar has completely dissolved.

Slice the tofu diagonally into strips and drizzle with the sauce. Sprinkle with sesame seeds and serve while still hot and crackling, alongside shredded cabbage and lemon wedges.