Drain the tofu, wrap each block in a clean kitchen towel, set them on a plate and press under the 30 cm / 12-inch skillet weighed down with two cans for 15 minutes. Use this time for steps 2 and 3.
Toast the rice in a dry 20 cm / 8-inch skillet over medium heat, shaking often, for 4 to 5 minutes until deep golden and fragrant. Grind in a spice grinder or mortar to a coarse sand texture. You'll have about 1 1/2 tbsp.
Slice the shallots and scallions, pick the mint and cilantro leaves, chop the mushrooms and peanuts, and thaw the edamame. Whisk the fish sauce, lime juice, brown sugar and red pepper flakes in a small bowl until the sugar dissolves. Wash and dry the lettuce leaves.
Unwrap the tofu and crumble it by hand into 1 cm / 1/2-inch pieces. Heat 2 tsp oil in the 30 cm / 12-inch cast-iron skillet over medium-high heat until shimmering. Add half the tofu in a single layer and sear for 5 to 6 minutes, stirring only every 2 minutes, until golden brown with crisp edges. Move it to a large bowl and repeat with 2 tsp oil and the rest of the tofu.
Add the last 2 tsp oil and the mushrooms to the empty skillet. Cook for 4 to 5 minutes until the liquid cooks off and the mushrooms brown. Return the tofu to the pan, add the edamame and stir for 1 to 2 minutes until warmed through.
Take the pan off the heat, pour the dressing over the filling and toss. Let it sit for 2 minutes so the tofu absorbs the dressing. If you want leftovers, scoop the portion to store into a container now. Fold the shallots, scallions, mint, cilantro, rice powder and half the peanuts into the rest.
Spoon about 1/3 cup of filling into each lettuce leaf, top with the remaining peanuts and serve with lime wedges. Eat within 10 minutes so the leaves stay crisp.