Wash and peel the radish, cut into 4 slightly thicker slices, the rest into thin slices. Salt the thin slices and let them steep. Preheat the grill. Line the tray with aluminum foil and brush a thin layer of oil. Place thick, unsalted radish slices on top, top with 1 goat cheese on each. Baked under the grill for 4 minutes. Dab the salted radish with kitchen paper, distribute on 4 flat plates. Drizzle with balsamic vinegar and olive oil. Sprinkle with capers and pepper. Add 1 radish slice with cheese each.