Heat the olive oil over medium heat in a large pot. Add onion and sauté until translucent, stirring frequently.
Add edamame and 4 cups vegetable stock. Bring to a boil, then turn heat down to medium-low and simmer until vegetables are tender, about 15 minutes.
Stir in arugula until wilted then remove from heat. Pour the soup into a blender and purée. Remove the top piece in the lid, so the steam can escape. Cover with a clean towel when blending so soup doesn’t splatter all over.
Pour soup back into the pot and salt and pepper to taste. Serve immediately.