Heat 1/4 inch of oil in a large skillet over medium-high heat.
Cut the zucchinis into ½ to ⅔ inch slices (I slice mine around 5/8" or 16 mm thick)
Place the flour, egg and panko crumbs into separate shallow dishes. Coat the zucchini in flour, shaking off any excess. Dip them into the egg, and then press the panko crumbs on both sides until well coated.
Place zucchini in the hot oil, and cook 3 minutes per side, until golden brown.
Make tonkatsu sauce by mixing ketchup and Worcestershire sauce.
Serve while hot with tonkatsu sauce.