In a large pot over high heat, boil the potatoes in the broth for 15 minutes, or until potatoes are tender. Carefully separate the potatoes from the broth and transfer to a blender or food processor.
Add 3/4 cup of the broth to the potatoes and puree for 5 seconds or more depending on how smooth you want the soup to be. Add remaining broth and set aside.
Melt the butter in a large saucepan over medium heat. Add the salt, ground black pepper, onion and dill weed to the butter, stir and saute for 2 minutes. Sprinkle with the flour and stir well.
Pour in the milk and heat until the mixture starts to thicken, about 1 to 2 minutes. Stir in the pureed potato mixture. Allow to heat through and serve.
