Step 1Clean the bok choy and remove any outer tough leaves. Steam until tender, 10 to 15 minutes.
Step 2Meanwhile, combine the rice vinegar, soy sauce, sugar, ginger, green onions and 2 tablespoons of sesame oil in a small bowl and set aside.
Step 3Heat a large, heavy, nonstick skillet over medium-high heat. Add 2 tablespoons of sesame oil. Cook the tofu on both sides until golden crispy edges form, about 3 minutes a side. Be careful not to break the tofu and do not crowd the pan. Use a small spatula to turn the slices. If they start to stick in the pan, add a little more oil.
Step 4Heat a 12-inch wok or skillet over high heat. Add 2 tablespoons of sesame oil. Cook the mushrooms until tender and lightly browned, 2 to 3 minutes.
Step 5Place the tofu slices down the middle of a large rectangular platter. Arrange the bok choy along one side of the platter and place the mushrooms on the other. Pour some of the sauce over everything; pass the rest at the table.