Prep all ingredients per the instructions above.
In a medium bowl, cover the sushi rice with cold water. Swirl with your fingers to release starch, then drain. Repeat 3 more times until water is mostly clear. Drain well.
Cook the rice according to package directions using a rice cooker or saucepan. Once tender, spread the rice on a small baking sheet. Sprinkle with vinegar and salt, then gently fold. Smooth in an even layer and let cool to room temperature.
In a medium saucepan, heat the vegetable oil over medium heat until it reaches 350°F (176°C).
In a bowl, whisk together flour, water, and egg until thick and just barely runny. Adjust with more flour or water as needed.
Pat the shrimp dry with paper towels. Dip each into the batter to coat, letting excess drip off. Carefully lower into the oil and fry, flipping halfway, for 2–3 minutes or until golden and crisp. Drain on paper towels.
In a pot of salted simmering water, cook the edamame pods according to package directions. Drain well. Drizzle with olive oil and sprinkle with coarse sea salt before serving.
Place a bamboo sushi mat on your surface. Lay one sheet of nori shiny side up. With wet fingers, spread an even layer of rice over the nori.
Lay plastic wrap over the bamboo mat and flip the rice-covered nori over.
Arrange shrimp tempura along the bottom edge of the nori, letting tails stick out slightly. Add thicker avocado slices and cucumber next to the shrimp.
Slowly roll the mat over the fillings, pressing gently to shape. Continue rolling until sealed.
Top each roll with alternating slices of thin avocado and mango.
Using a clean, damp knife, slice each roll into 8 pieces. Wipe and wet blade in between cuts to prevent it from sticking.
In a small bowl, whisk together mayonnaise and miso paste. Drizzle over the rolls and garnish with black sesame seeds.
In a blender, combine milk, matcha powder, and honey. Blend until smooth. Pour into glasses with ice.
Serve the dragon rolls with pickled ginger and edamame, and iced matcha latte.