Butter a 9 by 13 inch baking dish and preheat the oven to 350°F.
Place the vegetables in a large pot, cover with cold water and bring to a boil. Salt liberally. Cook until the potatoes are tender, 10-15 minutes. Drain well and return to the pot. Mash the vegetables, being concerned only that the potatoes are well mashed.
Stir in the cream cheese and Parmesan cheese and season with salt and pepper. Transfer the vegetables to the buttered baking dish and dot the top with butter. Bake for 45 minutes, until the top is lightly browned. You may prepare and refrigerate the casserole a day in advance. Remove from the fridge and bake for 1 to 1 1/4 hours until hot all the way through. Serves 6-8.