Celery root, also known as celeriac, tastes like a cross between celery and parsley.
Place celery root in a medium saucepan and cover with water. Season with salt and bring to a boil, then reduce to a rapid simmer. Cook, partially covered, until very tender and easily pierced, 15 to 25 minutes; drain.
Heat milk and butter in a small saucepan until butter is melted and mixture is hot.
Puree celery root and milk mixture in a blender until smooth, about 2 minutes. Strain through a sieve, pressing on solids with a rubber spatula to extract as much puree as possible. Season with salt and pepper. (If puree is too loose, cook, stirring, over medium heat until thickened to desired consistency.)