Place a steamer insert into a saucepan and fill with water to just below the bottom of the insert. Bring the water to a boil. Add the edamame, place a cover on the saucepan, and steam until just tender, 2 to 6.
Place steamed edamame in a food processor; blend until smooth. Transfer edamame puree to a large bowl.
Stir the shrimp, bok choy, egg white, ginger, soy sauce, 1 tablespoon sesame oil, garlic, and salt into the edamame puree.
Pour about 2 tablespoons water in a dish.
Scoop about 1 teaspoon of the shrimp mixture onto the center of a dumpling wrapper.
Wet the edge of the wrapper with water, then fold over to create a half-moon shape; pinch edge to seal.
Place the finished dumpling on a lightly floured baking sheet and cover with a damp towel; repeat with remaining wrappers.
Working in batches of 6 to 8 dumplings, heat about 1 tablespoon peanut oil in a large skillet over medium heat. Pan-fry dumplings until crispy on one side, about 2 minutes.
Flip dumplings and cook for 1 more minute. Add 1/4 cup water to the skillet and cover.
Steam dumplings until shrimp are bright pink and no longer transparent in the center, about 4 minutes more. Repeat with remaining dumplings.
For the dipping sauce: Whisk low-sodium soy sauce, sesame oil, green onion, sugar, rice vinegar, and red pepper flakes together in a shallow bowl until sugar has dissolved.
