Step 1

Combine maple syrup, salt, peppercorns, mustard seeds, and 8 cups water in a medium pot (make sure pork will fit comfortably inside). Stir brine until salt dissolves. Add pork; it should be completely submerged in brine. Cover and chill at least 12 hours.

Step 2

Do Ahead: Brine can be made 3 days ahead; cover and chill. Pork can be brined 2 days ahead; keep chilled.

Step 3

Combine vinegar, sugar, salt, and 1 cup water in a large bowl and stir until sugar and salt are dissolved, about 2 minutes. Add cabbage and massage for a few minutes with your hands to soften. Weight with a plate so cabbage is submerged. Cover and chill at least 1 hour. Drain cabbage before serving.

Step 4

Do Ahead: Cabbage can be pickled 2 days ahead. Keep chilled.

Step 5

Heat oil in a small saucepan over medium. Cook onion, garlic, and ginger, stirring occasionally, until onion is softened, 8–10 minutes. Add ketchup, soy sauce, brown sugar, mirin, and Worcestershire sauce and cook, stirring often, until mixture is reduced by a third, 6–8 minutes. Transfer to a blender and purée until smooth. Taste and season with salt if needed.

Step 6

Do Ahead: Sauce can be made 5 days ahead. Let cool; cover and chill.

Step 7

Place eggs, panko, and flour in separate shallow bowls. Using your hands, grind together panko to make the crumbs a bit finer. Line a rimmed baking sheet with paper towels and set a wire rack inside. Remove pork loin from brine and pat dry. Cut into 4 equal portions (about 1"-round medallions). Working with one at a time, place medallions in a large resealable plastic bag, seal bag, and gently pound without tearing meat to about ¼" thick.

Step 8

Working with 1 cutlet at a time, season lightly with salt and dredge in flour, shaking off excess. Dip in eggs, letting excess drip back into bowl, then coat in panko, pressing to adhere before shaking off excess. Transfer to a rimmed baking sheet.

Step 9

Pour oil into a large heavy skillet, preferably cast iron, to come 1" up sides. Heat oil over medium-high until an instant-read thermometer registers 350°–365° (don’t let the tip of the thermometer touch the bottom of the skillet). Carefully lower a cutlet along the side of skillet closest to you and let slide into oil away from you so it lies flat. Carefully swirl oil in skillet and cook just until cutlet is golden brown underneath, 1–2 minutes. Using tongs, carefully turn cutlet and cook until golden brown on the other side, 1–2 minutes. Transfer to prepared baking sheet. Repeat with remaining cutlets.

Step 10

Serve pork with bull-dog sauce, Kewpie mayonnaise, pickled cabbage, and radishes.