Place a wire cooling rack over a baking tray so that the excess oil can drip off of your tofu katsu once it's done frying. (If you don't have one, you can line a plate with paper towels instead.)
Heat about 1/2 - 1" of vegetable oil to about 375°F in a heavy-bottomed skillet or pot. (Use a Dutch oven or a skillet with higher sides if you want to avoid the splatter.) It is helpful to use a thermometer to ensure the tofu katsu cooks properly and doesn't turn out greasy.
Place the breaded tofu cutlets in the preheated oil and fry 3-5 minutes per side, until deep golden brown. Avoid over-crowding the pot, as this can lower the temperature of the oil and make it take much longer to cook, resulting in greasy katsu.
When golden brown, remove the tofu katsu to your prepared wire rack (or paper towel lined plate). Sprinkle with salt to finish.