For the pickled radish cubes: Combine the rice vinegar, water, superfine sugar and salt in a large bowl, whisking until the sugar and salt are dissolved. Add the radish cubes and toss to coat. Leave at room temperature, covered, for 24 hours. Then refrigerate.
For the pre-coating: In a large bowl, whisk together the cornstarch, salt, baking powder and pepper. Add the chicken and toss well until evenly coated in all areas. Transfer the chicken to a rack, shaking the chicken well to get rid of any excess coating. Let rest, uncovered, for 1 hour.
For the gochujang sauce: Combine the brown sugar, chile paste, soy sauce, rice vinegar, sesame oil, ginger and garlic in a saucepan and bring to a boil. Lower to a simmer and allow to cook over low heat for 3 to 4 minutes. Set aside.
For the sweet soy sauce: Heat the soy sauce, brown sugar, mirin, rice vinegar, sesame oil, ginger, chile flakes and garlic in a saucepan over medium heat until the sugar has dissolved; allow to simmer for 3 minutes. Mix the cornstarch with 1 1/2 tablespoons water and whisk into the sauce. Bring to a boil, and then remove from the heat and set aside.
For the batter: Pour enough oil into a 6-quart Dutch oven to reach a depth of 2 inches. Heat the oil over medium-high heat until a deep-fry thermometer inserted in the oil reads 350 degrees F.
In a large bowl, whisk together the cornstarch, matzo meal, flour, chile flakes, salt, garlic granules, onion granules and baking powder. In a smaller bowl, whisk together the water, vodka and chile paste. Just before frying, whisk the wet mixture into the dry mixture. The consistency should be relatively thin and runny.
Working in 2 batches, dip each piece of chicken into the batter, letting excess batter drip off. Suspend the chicken in the oil for a couple of seconds for it to set before letting it slip completely into the oil, otherwise the chicken will fall and stick to the bottom of the pot. Fry the chicken until golden brown and cooked through, 15 to 20 minutes per batch. Transfer to a wire rack to drain as done.
Serve with the sauces on the side.