Combine the soy sauce and sesame oil in a mediumsize bowl. Add the tofu and, with a rubber spatula, gently toss it with the marinade. Let sit 30 minutes.
In a large nonstick skillet, heat the tablespoon of oil over high heat until it is very hot but not smoking. Add the marinated tofu and spread it out so that it is in one layer. Fry it, shaking the pan often to prevent sticking, until it is a rich golden color all over. With a spatula, flip it over occasionally so it gets evenly browned. Place the tofu in a large bowl. Set the skillet aside.
Combine all the ingredients for the dressing in a jar with a tightfitting lid and shake vigorously. Pour half the dressing on the hot tofu and toss well. Chill the tofu until it is very cold, about 2 hours.
Meanwhile place the broccoli in the skillet, add a little water, and cover the pan. Cook until it is crisp yet tender, about 4 minutes. Immerse it in a bowl of cold water to stop any further cooking. Drain the broccoli thoroughly, then place it on a cotton or linen kitchen towel and pat it very dry. In a large bowl mix the broccoli, scallions, red pepper with half of the remaining dressing and toss well. Let sit at least 30 minutes to marinate. Just before serving mix in the tofu. Toss the mesclun with the remaining dressing, then place a portion of the greens on each large serving plate. Spoon a moundful of the vegetables and tofu in the center. Serve immediately.