With a sharp knife, cut tuna fillet crosswise at a slight angle and into slices about 1/4 inch thick. Wrap in a clean kitchen towel and set aside. Cut the cucumber into narrow strips about 4 inches long. Mix the sushi rice with the sesame seeds.

Just before rolling sushi, toast the nori by passing the shiny side over a high flame. The color of the nori will change from brownish black to dark green. (Without toasting, the nori will be gummy and hard to chew.) Cut toasted nori sheets in half crosswise.

Lay a 1/2 a sheet of the nori, shiny side down, on a bamboo rolling mat. Combine the rice vinegar and water in a mixing bowl, and moisten your hands with this hand vinegar to keep the rice from sticking to your hands as you work. Spread about 1 cup of the sushi rice on 3/4 of the nori closest to you, in a layer about 1/4 inch thick, spreading it to the edges. Smear a thin line of the wasabi across the center of the rice, and sprinkle with 1/2 teaspoon of chili oil. Lay 1/4 of the cucumber strips and 1/4 of the tuna slices evenly along the wasabi.

To roll, hold the line of ingredients in place with fingertips, and use thumbs to push up and turn the end of the bamboo mat so that the edge of the nori is lifted up and meets the far edge of the sheet. Correct the shape by gently but firmly pressing the bamboo mat around the roll for about 30 seconds to shape it. Make 3 more rolls.

Use a wet knife to cut each roll into 1-inch rounds. Arrange sushi on a platter or individual plates and garnish with the vinegared ginger.