1Bring a large pot of lightly salted water to a boil. Add edamame, boil for 5 minutes, then drain and rinse with cold water. Once edamame have cooled, remove the skins by squeezing each bean until the center pops out; discard the shells and set the beans aside.
2Heat oil in a saucepan over medium heat. Stir in onions and cook until they soften and turn translucent, about 5 minutes. Pour in chicken stock, bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer for 10 minutes. Add shelled edamame and continue cooking until the edamame and onions are both soft.
3Pour into a blender and carefully puree until smooth; or use a stick blender, and puree the beans in the saucepan. Return the puree to the saucepan and stir in milk and butter. Heat the soup through, about 5 minutes. Season to taste with salt and pepper.