Prepare a medium-hot fire for indirect cooking in a charcoal grill with a cover, or preheat a gas grill for indirect cooking to medium-high.
To make the patties, combine the shrimp, 1 cup of the panko, egg whites, salt, and pepper in a large nonreactive bowl. Form into 6 equal patties to fit the buns, cover, and refrigerate for 2 hours. Reserve the shredded coconut and remaining panko for later use.
To make the slaw, combine the vinegar, lime juice, fish sauce, soy sauce, sugar, oil, chile sauce, lime zest, garlic, onions, carrot, radish, salt, and pepper in a bowl and mix well. Let stand for 30 minutes. Just before assembling the burgers, add the cabbage and cilantro to the slaw mixture and toss. Taste, and add more salt and pepper, if needed.
To make the coconut sauce, combine the coconut milk, sugar, pineapple juice, lime juice, and lime zest in a small heatproof saucepan over low heat on the grill and cook until reduced by one third. Add the salt and pepper. Taste, and add more salt and pepper, if needed. Cover the pot and place it on the upper rack of the grill or off to the side to keep warm until needed.
Combine the reserved shredded coconut and remaining 1 cup panko in a pie pan. Dredge the patties in the mixture, pressing to adhere the coating.
Brush the grill rack with vegetable oil. Grill the patties over indirect heat, turning once, just until opaque throughout, 15 to 20 minutes. During the last few minutes of cooking, brush the buns with the butter and place on the grill rack until toasted lightly.
To assemble the burgers, spread the bun bottoms with the sauce, add the patties, and top with equal portions of the slaw. Add the bun tops and serve.
Makes 6 burgers
Suggested Wine Pairing: Pinot Grigio
Contestant Comments: My favorite Asian appetizer, coconut-crusted shrimp, made into a burger!
Anthony Czech, Decatur, Georgia