Press the tofu for at least 15 minutes to remove moisture.
In three separate bowls, prepare the breading stations: flour, plant-based milk (add cornstarch to the milk for extra crisp, if desired), and panko.
Dip each tofu slice into the flour, shaking off excess, then into the milk mixture, followed by the panko, pressing to coat well.
Heat oil in a large skillet over medium-high heat (oil should be about 1/4 inch deep and hot enough to sizzle when a drop of water is added).
Fry the tofu in batches for about 4-5 minutes per side, or until golden and crispy. Set aside on a paper towel-lined plate.
In a small saucepan, whisk together soy sauce, rice vinegar, maple syrup, ginger, and sesame oil over medium heat. Add water to thin slightly and simmer for 5-7 minutes, until glossy and slightly thickened. Remove from heat.
Serve each tofu katsu patty on a bed of steamed rice, drizzled generously with teriyaki sauce and garnished with pickled radishes or wasabi mayo if using.