Step 1Place 1 clove of garlic, the parsnip and celery root in a saucepan of salted water to cover.
Step 2In another saucepan, do the same with the remaining garlic, turnips and potatoes. Bring both to boil and cook, covered, until the vegetables are soft, about 25 to 30 minutes. Drain both. Puree the hot parsnip and celery root in a food processor; check for fiber. If there is any, press the puree through a sieve to remove it or pass it through a food mill.
Step 3Use a potato masher to mash the garlic, turnip and potatoes while hot; press through a sieve to remove any lumps or pass through a food mill.
Step 4Add the butter along with the puree. Stir in 2 tablespoons of the milk (or cream), the nutmeg, 1/4 teaspoon of salt and white pepper to taste. Add more milk if the mixture is too thick.
Step 5Taste; adjust seasonings. (This can be served immediately or transferred to an ovenproof or microwave-proof casserole and refrigerated overnight. Serve hot. Reheat, covered, in a 375-degree oven for 20 minutes or microwave until hot, about 5 minutes, stirring midway.)