Make the dressing: In a small bowl, whisk together the tamari, vinegar, lime juice, garlic, cane sugar, and sriracha.
Bring a small pot of salted water to a boil and place a bowl of ice water nearby. Blanch the snap peas by placing them in the boiling water for 1½ minutes, then scoop them into the ice water to stop the cooking process. Once cooled, drain, pat dry, and chop.
Assemble the bowls with the rice, shredded cabbage, carrot, cucumber, mango, black beans, pickled ginger, and basil. Top with the toasted peanuts, sesame seeds, and avocado, if using. Drizzle bowls with half the dressing and serve the rest on the side along with tamari and sriracha, if desired.