Place peeled shrimp in the bowl of a food processor fitted with blade attachment. Add Kewpie mayo, sliced scallions, cilantro, sliced garlic, ginger paste, sesame oil, sesame seeds, Kosher salt, and black pepper. Pulse until mixture is almost paste-like.
Transfer the shrimp burger mixture to a bowl, then stir in panko breadcrumbs. Place remaining panko on a small plate. Divide the shrimp into equal portions, shaping them into patties. Gently press each patty into the panko breadcrumbs, coating both sides very lightly.
Preheat an oven, then heat a nonstick skillet, griddle, or grill over medium-high heat. When hot, coat the surface with nonstick cooking spray, then add shrimp patties. Cook then transfer the skillet to the preheated oven and finish cooking.
Combine Kewpie mayo, Sriracha, and soy sauce in a small bowl, then stir until well mixed.
Spread a bit of spicy mayo on the bottom buns, then place a shrimp burger on top. Add lettuce, if using, then sliced avocado. Spread a bit more spicy mayo on the top buns, then place on top. Serve immediately!