Press the tofu: Wrap the tofu block in a clean kitchen towel and set a heavy pan or weighted plate on top for at least 15 minutes to press out excess water. This step keeps the crust from steaming soft once it hits the oil.

Cook the noodles: Boil the soba noodles according to package directions, about 5 minutes, then drain and rinse under cold water until they stop steaming. This stops the cooking and keeps them from clumping.

Cube the tofu: Cut the pressed tofu into 3/4-inch cubes. Even sizing helps every piece cook through at the same rate.

Coat in cornstarch: Toss the tofu cubes in cornstarch in a bowl until each piece is lightly and evenly coated. Shake off any excess before frying.

Fry the tofu: Heat oil in a large skillet over medium-high heat until it shimmers, then add the tofu in a single layer, frying in batches if needed. Cook until the edges turn deep golden, about 3 to 4 minutes per side.

Make the peanut dressing: In a bowl, whisk together peanut butter, soy sauce, rice vinegar, lime juice, honey, garlic, ginger, and sriracha until smooth. The mixture will look thick at first.

Thin the dressing: Add warm water a tablespoon at a time, whisking after each addition, until the dressing pours off a spoon in a smooth ribbon.

Combine noodles and vegetables: In a large bowl, toss the cooled noodles with carrots, cabbage, and edamame. Pour over most of the dressing and toss until every strand is coated.

Fold in the tofu: Add the crispy tofu cubes to the bowl and fold gently so the crust stays mostly intact.

Garnish and chill: Scatter scallions, cilantro, and crushed peanuts over the top, drizzle with the reserved dressing, and refrigerate at least 30 minutes before serving so the flavors settle.