Bring a large pot of salted water to a boil on high. Slice snow peas on an angle. Into pot, add linguine, snow peas, and edamame. Cook 3 min., until linguine is al dente and snow peas are tender. Drain in colander and rinse with cold water.
Meanwhile, peel and roughly chop ginger. Add to the bowl of a food processor with green onions, soy sauce, and rice vinegar. Pulse until ginger is minced. Through the feeder tube, add oil, and pulse until mixture is mostly smooth.
In a large bowl, add noodle mixture, ginger-green onion sauce, and carrots. Season with salt and pepper. Toss until well coated.