Put the celery root and rutabaga in a 4-quart saucepan with enough cool water to cover by at least 1 inch. Add 1 tsp. salt and bring to a boil. Turn the heat down and cook at a gentle boil, skimming off any white foam that rises, until the vegetables can be easily pierced with a fork, about 25 minutes.
Drain in a colander, letting the steam rise off for a few minutes. Meanwhile, heat the milk, butter, garlic, celery seed, and 1tsp. salt in the saucepan over low heat until the butter is melted.
For a rustic texture, return the celery root and rutabaga to the pan and mash with a potato masher to the consistency you like.
For a smooth texture, purée the celery root and rutabaga in a food processor until smooth, about 5 minutes, and then add them to the pan, stirring well to combine.
Season to taste with salt and white pepper and thin with additional milk, if necessary, before serving.