First, steam the beet whole until tender when pierced with a knife. Run cold water over the beet as you strip the skin off with a paring knife, then place the beet on a cutting board to cool slightly. Cut the beet in 1/2 inch slices, then stack them and slice in 1/2 inch strips. Place in a small storage tun with a lid and pour 2 tablespoons of the rice vinegar over, add a generous pinch salt, and toss to mix.
Slice the tofu into strips the same size, and place in the container with the beets. Put on the lid and flip the container to coat the tofu with beet juice and vinegar. Let the mixture marinate for at least an hour, turning occasionally.
Place the rice in a small pot with 1 1/2 cups cold water. Bring to a boil over high heat, then reduce to low and cook for about 30-40 minutes. When the rice is tender and all the water has been absorbed, take off the heat. Let stand for at least 5 minutes. Let cool.
When rice is cool, mix the remaining tablespoon of vinegar with sugar and drizzle over the rice. Fold in to coat.
Prep the vegetables and wrap your rolling mat with plastic wrap.
Place a nori sheet on the rolling mat, dampen the far edge, and place another sheet on that overlapping by an inch. Press to make one long sheet. Place the third sheet over the seam.
Spread rice over the nori, leaving an inch bare at the far edge. You'll use all of the rice. Arrange the fillings as shown in the photo, making even rows of each.
Start rolling up from the bottom, holding the fillings in place with your fingers as you use the mat to roll the nori and rice into an even cylinder.When you reach then end of the mat, carefully pull the roll back and keep going. Dampen the bare edge and turn the roll to sit on the seam.
Carefully slice in 6 fat slices and place on plates. Serve with wasabi, tamari, more pickled ginger, and whatever else sounds good.