We like the flavor of rice vinegar in the dipping sauce, but distilled white vinegar can be used instead. We prefer untreated shrimp, but if your shrimp are treated with salt or additives such as sodium tripolyphosphate (STPP), do not add the salt in step 2. Do not use unsweetened coconut or desiccated coconut.
FOR THE SPICY APRICOT DIPPING SAUCE: Combine all ingredients in a small bowl. Refrigerate until serving. (Sauce can be refrigerated for up to 24 hours.)
FOR THE COCONUT SHRIMP: Adjust oven rack to middle position and heat oven to 200 degrees. Line a rimmed baking sheet with parchment paper. Set a wire rack in a second rimmed baking sheet and line with a triple layer of paper towels. Sprinkle shrimp with ¼ teaspoon salt and baking soda in a bowl and toss to combine. Let stand for 15 minutes.
Meanwhile, place cornstarch in a bowl. Whisk egg whites and ¼ teaspoon salt in a second bowl until frothy and foamy, about 30 seconds. Combine coconut, panko, and remaining ½ teaspoon salt in a third bowl.
Working with 1 shrimp at a time and using the tail as a handle, dredge in cornstarch, dip into egg whites (rewhisk egg whites as needed so they remain foamy), and coat with the coconut mixture, pressing gently to adhere. Arrange breaded shrimp on the parchment-lined sheet. (Breaded shrimp can be refrigerated for up to 3 hours.)
Add oil to a large saucepan until it measures about 1 inch deep and heat over medium-high heat to 325 degrees. Add half of the shrimp, one at a time, to the hot oil. Cook, stirring gently to prevent pieces from sticking together, until shrimp are deep golden brown, 2 to 4 minutes. Adjust burner, if necessary, to maintain oil temperature between 325 and 350 degrees.
Using a spider skimmer or slotted spoon, transfer shrimp to the prepared wire rack and keep warm in the oven. Using the spider skimmer, remove any coconut from the oil. Return oil to 325 degrees and repeat with the remaining shrimp. Serve with dipping sauce.
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