Quick Pickled Beets provide a tangy marinade for the tofu, cutting a few steps on your way to showy, pretty handrolls.
To cook rice: Place the rice in a medium bowl and cover with cold water. Swish with your hands for a few seconds, then pour off the water. Drain in a wire mesh strainer.
Place the rice in a small pot with water and bring to a boil. When boiling, cover tightly and reduce the heat to low. Cook for about 30 minutes, depending on the variety. When all the water is absorbed and the rice in tender, take off the heat and let stand, covered, for five minutes. Spread on a plate to cool. Stir the vinegar and sugar in a cup, then drizzle over the rice, and fluff with a fork. Cover with a damp towel until time to use.
Trim the beet into a cube, and steam over simmering water. When tender when pierced with a knife, let cool. When cool enough to handle slice into 1/2 inch thick slices, then stack and slice into 1/2 inch wide julienne. In a storage tub, stir the vinegar, sugar and salt and add the beets, toss to coat. Marinate for at least 30 minutes.
Cut the tofu in strips in the same manner as the beets. Place in a bowl and drizzle with the marinade from the beets, and gently toss to coat.
Assembly: Use sharp scissors to cut nori sheets in half, reserve. Prepare a bowl of cool water with a shot of rice vinegar added, and have a clean towel for your fingers. On each nori sheet, place a couple tablespoons of rice on one half. With wet fingers, pat the rice to cover a square area at one end of the nori, leaving the remaining portion exposed. The corner of the square of rice that is closest to the center is the point of the cone. From that corner, place a leaf of lettuce, pickled ginger, a piece of beet, a piece of tofu, and mayo, if desire . Roll the rice around the fillings, keeping the point of the cone closed. Dab some vinegar water on the exposed nori and dry your fingers. Roll the nori around the cone and press to seal.