Peel celery root using a vegetable peeler or knife (or both). Cut into 1-inch chunks and place into a large pot. Cover with water and heat to boiling.

Once boiling, reduce heat and simmer for about 45 minutes, until tender.

Drain and return to pot. Mash celery root, then add butter and milk and mash or beat until desired smoothness is achieved. (You can also pulse in a food processor, if you like.)

Stir in parsley, salt, thyme, and black pepper. Taste and adjust seasoning. Serve with additional butter, if you like.