Lightly butter ten 1/4-cup ramekins or an 8-by-12-inch glass baking dish. In a medium saucepan, steam the parsnips until very tender, about 25 minutes.
Transfer the parsnips to a food processor and puree. Strain the puree through a coarse sieve into a medium bowl.
Whisk in the eggs, milk, cream, salt and pepper. Strain the custard through a fine sieve and pour it into the ramekins or the baking dish. Set the ramekins or the baking dish in a large roasting pan and carefully pour in enough hot water to reach halfway up the sides of the ramekins or the baking dish. Cover the pan loosely with foil.
Bake for 45 minutes for the ramekins and 1 hour for the baking dish, or until the custards are just set.
Make Ahead: The custards can be refrigerated overnight. Reheat in the ramekins or baking dish in a microwave oven on high until warmed through.
