Prepare 3 bowls for breading. Place flour in the first bowl with a pinch each of kosher salt and black pepper. In the second bowl, whisk together eggs and water. In the third bowl, combine panko and coconut with 1/2 teaspoon each kosher salt and black pepper.
Pat shrimp with paper towels to remove excess moisture. One at a time, dredge shrimp in flour, shaking off excess. Dip into egg wash, allowing excess to drip off. Dip in coconut-panko mixture, gently pressing to adhere.
Heat 2-3 inches of oil in a heavy-bottomed, deep pot to 325 to 350 degrees F. Fry shrimp in batches of 5-6, being sure not to crowd the pot, until the breading is golden and the shrimp are opaque, 3-4 minutes. Use a spider strainer to gently move the shrimp around in the oil for even browning.
Remove shrimp from the oil with the spider strainer and place them on a double layer of paper towels set on a plate or baking sheet to drain.
Preheat oven to 425 degrees F with rack in the lower-middle position.
Place shrimp in a single layer on a baking sheet. Spray both sides with vegetable oil spray (I use an oil spray bottle.)
Bake for 8-10 minutes, until breading is light golden and shrimp are opaque, turning the shrimp over once halfway through baking.
Spray shrimp on both sides with vegetable oil spray, as in the baking method. Add shrimp to the air-fryer basket (I like to cook them in batches of 6-7) and fry at 400 degrees F for 6-8 minutes, until breading is golden and shrimp are opaque. Flip shrimp over once during air frying.
Place Coconut Shrimp on a serving platter and garnish with sliced scallions or chopped cilantro, if desired. Serve hot with dipping sauce.
*Note: nutrition estimates below are for deep-fried shrimp, assuming 10% oil absorption. Values are for the shrimp only and do not include the dipping sauce.Prep-ahead: If you're entertaining, you can bread the shrimp up to 4-6 hours in advance and store them on a baking sheet in the refrigerator. Depending on how chilled they are when you cook them, you might need to add a minute to the cooking time.Variation:To add a little spice to your breading, whisk 1/2 teaspoon cayenne pepper into the flour.See the blog post above for information on shrimp sizing, comparisons of cooking methods, and reheating suggestions.