Mix together the tuna, mayonnaise and wasabi in a bowl until well combined.
To roll the sushi, cover a bamboo sushi rolling mat with plastic wrap. Lay a sheet of nori, rough side up, on the plastic wrap. With wet fingers, firmly pat a thick, even layer of seasoned sushi rice on top of the nori and cover it completely.
Place 2 slices of cucumber in a line along the bottom edge of the sheet, then spread a line of tuna mixture alongside the cucumber.
Pick up the edge of the bamboo rolling sheet and fold the bottom edge of the sheet up to enclose the filling. Tightly roll the sushi into a thick cylinder.
Once the sushi is rolled, gently squeeze to compact it tightly.
Repeat to make a second roll.
Cut the rolls with a very sharp knife into 5 or 6 pieces each and serve them with soy sauce, pickled ginger and wasabi on the side.
To ensure your rolls are neatly cut, use a very sharp knife and slightly wet the blade before each cut.