To make the burgers, in a large bowl, mix together the chicken, mayo, 1/2 cup bread crumbs, mustard, sriracha, garlic, ginger, and a large pinch of salt and pepper until evenly combined. Divide the mixture into four even portions and then shape each one into a thin burger patty. Place on a baking sheet, lined with parchment paper, and chill for at least 30 minutes.
When ready to cook, whisk the eggs in a shallow dish. Then add the remaining bread crumbs into a separate shallow dish. Dip the chilled burger patties, one by one, into the egg and then into the bread crumbs, flipping over to coat evenly. Return to the baking sheet and continue coating the remaining patties.
Fill a large skillet with about 2-inches of oil and heat over moderate heat. Once hot carefully place one or two patties into the oil and fry until golden brown on both sides and fully cooked in the middle. It should register at 165°F with an instant read thermometer. Carefully remove from the oil and transfer to a wire rack set over a baking sheet. Keep warm in a 250°F oven while you continue to fry the remaining burger patties.
To assemble the burgers, toast the buns in a dry skillet, cut side down. Then spread the bottom halves with Dijon mustard and top each with a crispy burger patty. Top with cabbage, radish slices and tonkatsu sauce (recipe follows). Place the top bun on and serve immediately. Enjoy!
For the tonkatsu sauce, in a small saucepan, combine the ketchup, soy sauce, sugar, mirin, sriracha, Worcestershire sauce, ginger and garlic. Set over low heat, bring to a simmer and cook for 5 minutes. Remove from heat and allow to cool completely.