In a tall stockpot, bring all the ingredients except the salt, pepper and butter to a boil. Lower the heat and simmer for 30 minutes, or until each vegetable is easily pierced with the tip of a knife.
Pass the soup through the medium disc of a food mill. Or skim the vegetables out of the liquid, pulse to a coarse puree in a food processor, and recombine the vegetables and liquid. Season with salt and pepper. The soup can be refrigerated at this point for up to 3 days, or frozen for up to 2 months.
Bring the soup to a simmer. Stir in the butter just before serving.