Cook the noodles:
Bring a medium potful of water to a rolling boil. Add the rice vermicelli and, stirring often, cook them until the strands are soft and white, but still resilient, 3 to 5 minutes. Don't be tempted to undercook them, as they must be fully cooked to absorb the flavors of the dish. Rinse them in a colander under cold water just until they're cool and the water runs clear. Let the noodles drain in the colander for 30 minutes, and then set them aside for up to 2 hours, unrefrigerated.
Cook the tofu and vegetables:
Heat 2 Tbs. of the oil in a nonstick pan or skillet over medium heat. Add the tofu pieces and stir-fry until nicely browned. Remove and drain on paper towels. When cool, cut them into bite-size strips. Set aside.
Heat the remaining oil in a large skillet or sauté pan over high heat. If the pan is smaller than 12 inches, cook the vegetables in two batches. Wait until the oil gets very hot, almost smoking (the vegetables should sizzle during the entire cooking time), and add the shallots, constantly stirring until they become fragrant, about 20 seconds. Add the mushrooms and stir-fry for another 20 seconds. Add the broccoli, cabbage, and bok choy, stir for 30 seconds, and add the red bell pepper. (If the pan gets too dry, sprinkle in 1 to 2 Tbs. water.)
Working quickly, create an open space in the middle of the pan by pushing the vegetables against the edges. Add the soy sauce to the open area. It should sizzle and caramelize slightly, creating a distinctive aroma. Stir the vegetables with the soy sauce a few times and remove from the heat. Toss the vegetables with the tofu.
Assemble the salads:
Divide the lettuce, bean sprouts, cucumber, mint, and basil among four large soup or pasta bowls. Fluff the noodles with your fingers and divide them among the prepared salad bowls. Put the tofu and vegetables on the noodles and garnish each bowl with the peanuts and cilantro. Pass the nuoc cham at the table; each diner should drizzle about 3 Tbs. over the salad and then toss the salad in the bowl a few times with two forks or chopsticks before eating.