Heat 2 tbsp 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 saute 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 tbsp 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.