Bring 8 cups (2 quarts) of water to a boil in a large saucepan. Add a big pinch of coarse salt and then the edamame beans. Boil until the beans turn bright green, 1 minute. Drain into a colander, shaking to remove excess water.
Let the beans cool for 2 minutes, and then toss with the salt and dill, tossing to coat. Add the pea shoots, toss briefly and serve immediately with a small dish alongside for collecting the shells.