Preheat a grill to medium high. Mix the kimchi and mayonnaise in a small bowl; set aside. Combine the ground beef, garlic, brown sugar, soy sauce, sesame oil, 1 teaspoon salt and a few grinds of pepper in a medium bowl. Form the beef into 4 patties, about 4 inches wide and 3/4 inch thick.
Oil the grill grates. Add the patties and cook until marked on the bottom and starting to cook up the sides, about 3 minutes. Flip and cook 3 to 4 more minutes for medium rare.
Toast the buns on the grill. Transfer the burgers to the bun bottoms. Top with the kimchi mayonnaise, pickles and bun tops. Serve with chips.