Heat oven to 300 degrees. Whisk together egg yolks and sugar until very smooth. Place mixture into the top of a double boiler; be careful not to cook the eggs. In another saucepan, scald cream. When both liquids are hot (but not cooked or boiled), slowly whisk cream into eggs.
In a small blender, mix turnip and a dollop of cream and blend well. Add turnip to egg/cream and mix well. Use a sieve to strain out lumps. Add vanilla.
Pour mixture into ramekins or small souffle dishes. Place in warm water on a deep cookie sheet or baking pan. Bake 1 hour. Custard is done when well set. Let cool completely (up to 8 hours). Just before serving, sprinkle tops with brown sugar (about 1 teaspoon per dish) and use a browning torch to crisp.