Prepare the dredging station. In the first bowl, mix the flour and white pepper together. In the second bowl, beat the eggs. In the third bowl, toss together the panko breadcrumbs and coconut, until well-combined.
Dunk the shrimp in the flour first, coating on both sides. Holding the shrimp by the tail, dip it fully into the egg mixture. Finally, dredge the shrimp in the panko-coconut mixture, pressing firmly to coat each side. Repeat the steps with the remaining shrimp.
In a frying pan, add ¼ inch of oil. Heat over medium, until a bit of flour sizzles immediately.
Add the shrimp to the hot oil, and fry until golden brown, about 3 minutes per side. Remove from the skillet, and place the shrimp on a paper towel-lined plate. Serve warm with your favorite sauce.