Remove end of celery root, then peel remaining and cut into 1-inch pieces. Peel and core parsnip, then cut into 1-inch pieces. Place celery root and parsnip in a steam basket and set over a pot of boiling water and cover pot. Steam vegetables until very tender, 15-20 minutes.
Transfer vegetables to a food processor with cream, butter, salt, and pepper, and pulse until very smooth, about 1 minute. Season with salt and pepper.