Make the quick-pickled radish. Thinly slice 3 medium radishes about 1/16 inch thick. Combine ½ teaspoon sugar with a pinch of salt, 2 tablespoon rice vinegar, and 2 tablespoon hot water, stirring until the sugar has dissolved. Add the sliced radish and let sit for 30 minutes.
Prepare the scallion lime aioli. Blend together ½ cup mayonnaise with 4 scallions, and the juice of ½ lime until smooth. Season with salt and pepper. Set aside.
Make the beef patties. Season 1 lb ground beef with ¼ cup grated onion, 2 teaspoon minced garlic, 1 teaspoon minced ginger, 1 ½ tablespoon soy sauce, 2 tablespoon brown sugar, and ½ teaspoon black pepper until well combined. Shape the beef into 6 patties, about ¼ cup each.
Heat a grill or saute pan over medium-high heat. Add 1 tablespoon oil and add 1 cup chopped kimchi. Cook until the kimchi has caramelized, about 4-5 minutes. Remove the kimchi and keep warm.
Wipe the pan clean and cook the beef patties until the desired degree of doneness.
Assemble the sliders. Toast the slider buns and stack the bottom bun with the beef patty, scallion lime aioli, sauteed kimchi, fresh Asian pear, and pickled radish. Serve warm.