To make the spicy mayo, combine Kewpie mayonnaise in a small bowl with Sriracha and soy sauce. Stir well, taste, then add more Sriracha if you want it spicier. Set aside.
Heat neutral oil over medium-high heat in a large skillet. When hot, add peeled, deveined raw shrimp. Season with Kosher salt and black pepper. Cook until the shrimp turn pink. Flip the shrimp over, then add ginger paste, garlic clove, soy sauce, and the juice from lime. Cook, stirring to mix together the sauce.
Divide the rice evenly between 4 bowls, then top each with some of the cooked shrimp. Add cubed avocado, then garnish with thinly sliced scallions, cilantro, and sesame seeds. Add any additional toppings you like, then drizzle generously with spicy mayo. Serve immediately with seaweed square.