How to Make It
In a large bowl, beat the eggs. Stir in the mascarpone until blended. Add 1/2 cup of the drained kimchi, two-thirds of the minced garlic, 1/2 teaspoon of salt and the ginger. Fold in the crabmeat and 1/2 cup of the panko or plain dry bread crumbs. Pat the crabmeat mixture into 6 burgers, cover with plastic wrap and refrigerate until the crab burgers are chilled and firm, about 30 minutes.
Meanwhile, in a small bowl, mix the mayonnaise with the lime juice, sambal oelek, mustard, lime zest and the remaining minced garlic. Season with salt and pepper. In a large bowl, toss the endives with the carrot, the remaining 1 cup of kimchi and 2 tablespoons of the pickling juice.
Spread the remaining panko on a plate and coat the burgers. In a very large nonstick skillet, heat 1/4 inch of oil. Add the burgers and cook over moderately high heat, turning once, until browned, 7 minutes. Drain on paper towels.
Spread the mayonnaise on the toasted brioche. Set the crab burgers on the brioche toast and top with the kimchi slaw. Close the crab burger sandwiches and serve.
Kimchi (spicy pickled and fermented cabbage) and sambal oelek, an Indonesian chili-garlic sauce, are both available at Asian markets and specialty shops.