In a small bowl, mix rice vinegar, sugar, and salt until dissolved. Gently fold into warm cooked rice. Let cool slightly before rolling.

In a small saucepan, combine soy sauce, mirin, and sugar. Simmer over medium heat until thickened, about 5–7 minutes. Let cool.

Place a bamboo sushi mat on a clean surface and cover it with plastic wrap. Place one sheet of nori (shiny side down) on the mat.

Wet your fingers slightly to prevent sticking. Spread a thin, even layer of sushi rice over the nori. Sprinkle sesame seeds over the rice, then carefully flip the nori over so the rice faces down.

Along the bottom edge of the nori, place 2 shrimp tempura and a few cucumber strips. Roll tightly using the bamboo mat, pressing gently to form a firm cylinder.

Layer thin avocado slices across the top of the roll. Use plastic wrap and the mat to gently press them down so they stick.

Remove plastic wrap. Cut the roll into 8 even pieces using a sharp, wet knife. Arrange on a platter, drizzle generously with eel sauce, and serve with pickled ginger and wasabi.