Peel the celeriac root and wash any extra traces of dirt off. Wash the potatoes well. *note, I like to leave the peels on for extra texture, but you can peel your potatoes if you like.
Cut the celeriac and potatoes into medium sized pieces. Put into a large cooking pot and cover with water. Bring to a boil and then reduce head to a simmer. Cook until soft enough to mash, about 30–40 minutes. Drain and let sit covered in the same pot that you used to cook them in, for about 5 minutes to remove excess water.
Add cream, butter and then mash. I like to use a hand held masher as I prefer some texture to our mashed potatoes. Feel free to use whatever suits your personal taste. Stir in the parsley. Season to taste with salt and pepper.