Combine the rice and boiling water and cook until all the water is absorbed, about 50 minutes. Stir in the seasoned rice vinegar and tamari soy sauce; set aside to cool.
Cut the carrot, cucumber, bell pepper, avocado, and spinach into shoestring strips.
Lay a sheet of nori on a sushi mat and spread it with about 3/4 cup of cooked sweet brown rice, leaving a 3/4-inch strip uncovered on the top and bottom. Form a little trough from side to side in the middle of the rice bed and lay 4 or 5 strips of each of the vegetables into it, allowing some of them to stick out the ends. Brush the top and bottom edges of the nori with a small amount of the wasabe mixture, then roll the nori up as tightly as you can. Repeat with additional nori sheets until all the rice is used.
To serve, slice across the roll in whatever thickness you desire (about 1 inch gives you 6 per roll). Garnish with the pickled ginger.