Bring a large pot of water to a boil. Have ready 2 bowls of ice water. When water boils, add 1 tsp. salt, peas and edamame and bring back to a boil. Cook until tender, 3 to 4 minutes. Using a slotted spoon or sieve, transfer vegetables to a bowl of ice water. Add sugar snap peas to pot of water and bring back to a boil. Cook until just tender, about 30 seconds. Transfer to other bowl of ice water, reserving boiling water. Once vegetables are cold, drain well. Cut sugar snap peas into fourths crosswise.
In a serving bowl, whisk together lemon juice, vinegar and mustard. Add oil in a slow stream, whisking until thickened and well combined. Stir in shallot and tarragon. Season with 1 tsp. salt and 1/2 tsp. pepper.
Cook pasta in reserved pot of boiling water until al dente, about 12 minutes or according to package directions. Drain pasta well and immediately transfer to bowl with vinaigrette. Add vegetables and cheese. Gently toss together until pasta is well coated. Season with additional pepper, if desired. Serve at room temperature.