Cook the potatoes and parsnips in salted boiling water until cooked through but not falling apart. Drain them, and transfer them to a large bowl. Meanwhile, heat the butter, cream and buttermilk in a nonreactive sauce pot. Add the cream mixture and the salt and pepper to the potatoes. If using a hand mixer, work on low speed and mix the potatoes and parsnips until smooth and well combined. If you like, run the mixture through a food mill in order to remove any lumps. Serve immediately.