Prepare Sushi Rice: Rinse sushi rice under cold water until water runs clear. Cook rice according to package directions. Mix rice vinegar, sugar, and salt in saucepan over low heat until dissolved. Transfer cooked rice to large bowl, gently fold in vinegar mixture using cutting motion. Fan rice while mixing to cool. Cover with damp towel.
Make Tempura Shrimp: Heat 2 inches vegetable oil to 350°F. Prepare tempura batter according to package directions. Pat shrimp completely dry, dip in batter. Fry shrimp for 2-3 minutes until golden. Drain on paper towels.
Prep Toppings: Slice avocados lengthwise into very thin slices (⅛ inch thick), keeping slices attached at one end. Heat pre-cooked eel according to package directions. Slice eel into long strips about ½ inch wide.
Roll Inside-Out Sushi: Place bamboo mat covered with plastic wrap on work surface. Put nori sheet shiny side down. With wet hands, spread ¾ cup sushi rice evenly over nori, leaving ½-inch border at top. Sprinkle sesame seeds over rice. Flip so nori is on top. Place 2 tempura shrimp lengthwise across center with cucumber strips alongside.
Roll and Seal: Using bamboo mat, lift edge closest to you and roll over filling, tucking tightly. Apply gentle, even pressure with mat as you roll away from you. Give final squeeze to seal. Keep wrapped in mat while prepping topping.
Create Dragon Design: Unwrap roll and transfer to cutting board. Lay fanned avocado slices across top of roll, slightly overlapping to create scales. Place eel strips between avocado slices. Gently press plastic wrap over top and use sushi mat to press everything together.
Slice and Serve: Using sharp knife dipped in water, cut roll into 8 equal pieces, wiping knife between cuts. Arrange on platter, drizzle with eel sauce, add spicy mayo dots, garnish with black sesame seeds and tobiko. Serve with soy sauce, wasabi, and pickled ginger.