Preheat oven to 450°.
Combine the eggs, granulated sugar, brown sugar, salt, and spices. Beat well. Blend in the turnip, then add cream and beat well. Pour into pastry-lined pan. Bake for 10 minutes, then reduce temperature to 350° and continue baking for 40 to 45 minutes. The pie is done when a knife inserted into the center comes out clean.