In a small bowl, whisk together the mayonnaise, sriracha, ketchup, lime juice, coconut aminos, pressed garlic clove, and salt until smooth and well combined. Set aside at room temperature. This sauce is the heart of the dish, so make sure the flavors are well balanced—taste it and adjust the sriracha or lime juice to your preference before using it.
In a shallow bowl, combine the coconut flour, arrowroot powder, salt, black pepper, and smoked paprika. Whisk together to ensure the seasonings are evenly distributed throughout the dry mixture. Place the whisked eggs in another shallow bowl next to the breading mixture. This setup makes the coating process quick and efficient.
Working with a few shrimp at a time, dip each shrimp into the whisked egg, allowing excess to drip off, then immediately dredge it in the breading mixture from Step 2, making sure both sides and the tail are fully coated. Place coated shrimp on a clean plate. I like to coat all the shrimp before I start frying—this way you're not juggling raw shrimp and hot oil at the same time, which keeps things safer and more organized.
Pour enough coconut oil into a large skillet to reach about 1/4 inch up the sides and heat over medium-high heat until the oil shimmers and is hot but not smoking (about 2-3 minutes). Working in batches to avoid overcrowding, carefully place coated shrimp into the hot oil and fry for 2-3 minutes on the first side until golden brown, then flip and fry for another 1-2 minutes until the second side is golden and the shrimp are cooked through. Transfer cooked shrimp to a paper towel-lined plate to drain any excess oil.
Add all the cooked shrimp from Step 4 to a large bowl and pour the bang bang sauce from Step 1 over them. Using a spatula or wooden spoon, gently toss the shrimp until every piece is evenly coated with the creamy, spicy sauce. The warmth of the freshly fried shrimp will help the sauce coat beautifully.
Transfer the sauced shrimp to a serving platter or individual plates. Scatter the thinly sliced green onions generously over the top, followed by a sprinkle of sesame seeds for color and a nutty finish. Serve immediately while the shrimp are still warm—I find the contrast between the warm, crispy shrimp and the cool, creamy sauce is what makes this dish so irresistible.