Cook edamame in a 3-quart pot of boiling salted water 5 minutes. Drain in a sieve and rinse under cold running water to stop cooking. Drain edamame again and pat dry.
Whisk together vinegar, water, salt, and pepper in a small bowl until salt is dissolved.
Add oil in a slow stream, whisking until combined.
Toss together edamame, escarole, and mint in a large bowl.
Add cheese and drizzle salad with dressing, then toss again. Serve immediately.