Prepare the beets: Preheat the oven to 400°F. Place the whole beets on a piece of foil and drizzle with olive oil and pinches of salt. Wrap the beets in the foil and roast on a baking sheet for 45 to 60 minutes, or until soft and fork-tender. The time will depend on the size and freshness of the beets. Remove the beets from the oven and remove the foil. When they are cool to the touch, peel the skins. I like to hold them under running water and slide the skins off with my hands. Slice the beets lengthwise into ¼-inch strips.
In the bottom of a small baking dish or shallow bowl, combine the rice vinegar, tamari, sesame oil, and ginger. Add the beets, toss to coat, and set aside to marinate. After 15 minutes, toss again to ensure even coating.
Make the rice: Cook the rice according to the directions in this post. Mix the cooked rice with the vinegar, sugar, and salt.
Assemble the rolls: Place a small bowl of water and a kitchen towel near your work area as your hands will get sticky. Place one nori sheet, glossy side down, onto a bamboo mat and press a handful of rice onto the lower two-thirds of the sheet. At the bottom of the rice place a row of beets, cucumber, and avocado. Don’t overfill or it will be more difficult to roll. Use the bamboo mat to tuck and roll the nori. Once rolled, use the bamboo mat to gently press and shape the roll. Place the roll to the side, cut-side down. Repeat with remaining rolls.
Use a sharp knife to cut the sushi. Wipe the knife clean with a damp towel between cuts.
Sprinkle with sesame seeds. Serve with tamari, pickled ginger, and vegan mayo mixed with a little sriracha, if desired.