Peel carrots and cut into chunks. Boil or steam until tender, then puree in a food processor. Strain through a medium sieve. Measure 1 3/4 cups of carrot puree. Stir in the cinnamon, nutmeg, salt and white pepper.
Make a bechamel by melting the butter over low heat and stirring in the flour for about two minutes. Add the milk to the flour-and-butter mixture. Whisk until fluffy. Remove from the heat and allow to cool till lukewarm.
Stir the egg yolk and carrots into the bechamel and whisk until well blended.
Beat the egg whites with the cream of tartar in a clean bowl with clean beaters. When it makes soft peaks, add the sugar and beat a bit more until the peaks are stiff and no gritty sugar remains.
With a rubber spatula or wooden spoon, stir the beaten egg whites into the carrot mixture until well distributed. Fine streaks are okay.
Bake in a greased baking dish at 350 degrees for 35-45 minutes, or until a knife pushed into the center comes out clean. You can also bake these in individual custard cups or au gratin dishes, but the baking time will be reduced by about half.
