Make the quick-pickled radish. Thinly slice radishes about 1/16-inch thick. Combine sugar with a pinch of salt, rice vinegar, and 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 mayonnaise with scallions, and the lime juice until smooth. Season with salt and pepper. Set aside.
Make the beef patties. Combine ground beef with grated onion, minced garlic, minced ginger, soy sauce, brown sugar, and black pepper in a large bowl. Shape the beef into 8 patties, about ¼ cup each.
Heat a grill or saute pan over medium-high heat. Add 1 tablespoon oil and add 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 scallion lime aioli, beef patty, sauteed kimchi, fresh Asian pear, pickled radish, and extra aioli. Serve immediately.
Notes
The scallion lime aioli, sauteed kimchi, and pickled radish can be prepared the day before.