In a large pot or Dutch oven melt the butter over medium heat. Add the carrots, celery, and onions and saute for 3-5 minutes or until slightly tender. Add the broth, potatoes and thyme. Cook over medium heat for 15 minutes or until the potatoes are tender, and not mushy. Using a potato masher, spatula or large spoon, mash about ⅓ of the potatoes to thicken. Reduce the heat and stir in 2 cups of the milk, corn, salt, parsley, cayenne and black pepper.