How to Make It
Put the tofu on a rimmed baking sheet and top with another baking sheet. Set 2 large, heavy cans on the sheet and press the tofu for 30 minutes. Drain the tofu and cut it into 1/2-inch dice.
In a small bowl, stir the lime juice with the fish sauce, 1 tablespoon of the soy sauce, the sugar and the crushed red pepper.
In a medium skillet, heat the oil. Add the garlic and cook over moderately high heat until fragrant, about 30 seconds. Add the shiitakes and cook, stirring, until softened, about 1 minute. Add the remaining 2 tablespoons of soy sauce and cook over moderate heat until the shiitakes are tender, about 4 minutes longer.
Transfer the shiitakes to a medium bowl. Add the diced tofu, raw green beans, scallions, shallot, cilantro, mint and the dressing and toss. Spread the lettuce leaves on a platter. Spoon the salad over the leaves and serve.