Cut a 2-cm (3/4-inch) strip off the largest side of the seaweed sheet to shorten it slightly.
On each sheet, spread about 125 ml (1/2 cup) of rice on the matte side of the nori, up to 2-cm (3/4-inch) from one edge of the narrow side, working with moistened fingers. Lightly moisten countertop. Flip sheets, rice side down.
For the first roll, spread julienned cucumber on the top third of the nori. Roll, starting with the rice-less side of the roll. Compress roll with a bamboo mat, applying uniform pressure. Sprinkle with fried tempura. Dip the tip of a knife in water and cut roll into ten pieces. Place on a serving plate.
For the second roll, work again with rice side down. Place avocado pieces on the upper third of the nori sheet. Start rolling with the rice-less side first. Compress roll with a bamboo mat, applying uniform pressure. Sprinkle with tempura. Dip the tip of a knife in water and cut roll into ten pieces. Place next to the cucumber rolls.
Serve with soy sauce or Japanese mayonnaise, and wasabi.
This recipe was developed in collaboration with Genevieve Everell.