Combine carrots, radish, cucumber, vinegar, sugar, and 1/4 teaspoon salt in a small bowl. Refrigerate for at least 1 hour.
Pulse avocados, ginger, 2 tablespoons water, lime juice, and garlic in a blender. Continue to process until sauce has the consistency of aioli, adding up to 2 tablespoons more water, 1 tablespoon at a time, if necessary. Transfer to a container with a tight-fitting lid.
Heat a medium cast-iron skillet over medium-high heat. Add oil. Place tofu in a single layer in skillet. Cook until brown, 8 to 10 minutes. Season with salt and pepper. Let cool.
Prepare rice noodles according to package directions. Drain and rinse.
Toss pickled vegetables with noodles, then divide among 4 bowls. Top with tofu, bean sprouts, and cilantro. Drizzle with avocado sauce. Garnish with peanuts and sriracha, if desired, and serve.
Recipes from The No Meat Athlete Cookbook: Whole Food, Plant-Based Recipes to Fuel Your Workouts and the Rest of Your Life. Copyright © 2017 Matt Frazier and Stepfanie Romine. Reprinted by permission of The Experiment.