In a small bowl, whisk together flour, salt, and peppers. In a second bowl, whisk eggs until well beaten. Stir bread crumbs and coconut together in a third bowl.
Add 1/2-inch oil to a Dutch oven or large skillet set over medium-high heat.
Dredge shrimp in flour, then egg, and finally the coconut-breadcrumb mixture. Set aside on a plate and repeat with remaining shrimp.
When the oil reaches 350 degrees F, fry shrimp in batches of 5-6 at a time for 2-3 minutes on each side until golden brown and crispy.
Transfer fried shrimp to a paper towel-lined plate to drain; repeat process with remaining shrimp. Garnish finished shrimp with chopped cilantro or parsley, and serve with dipping sauce.
Cilantro Lime Aioli:
Combine all ingredients in a small food processor or blender and mix until well combined.