Place edamame in a large saucepan. Cover with water to 2 inches above beans; bring to a boil and cook 10 minutes or until soft. Drain; set aside.
Place half of edamame, 1/2 cup broth, and shallots in a blender or food processor; process until smooth. Pour puréed shallot mixture into a large bowl. Combine the remaining edamame, 3/4 cup broth, and avocados in blender or food processor; process until smooth. Add puréed avocado mixture to puréed shallot mixture; stir to combine. Add 3/4 cup broth, water, juice, salt, and pepper to puréed mixture; stir well with a whisk. Cover and chill. Serve with parsley and lemon wedges, if desired.