Melt butter in a Dutch oven over medium heat. Add onion and sauté until translucent and softened, 8 minutes. Sprinkle in flour and cook, stirring frequently with a wooden spoon or heatproof spatula, 3 minutes more. Add potatoes and chicken broth and bring to a simmer. Continue to simmer mixture until potatoes are tender, 8 to 10 minutes. Add peas and simmer for 2 minutes.
Puree soup in a blender or food processor; divide into batches if necessary. Return soup to Dutch oven and stir in cream, parsley and dill. Season soup with salt and pepper and serve hot.