Step 1Cut the vanilla bean into extremely small pieces with scissors. Put the vanilla bean pieces and 3 tablespoons sugar in a mortar. Crush together with a pestle. Strain through a fine sieve, add another 3 tablespoons sugar and repeat the process.
Step 1Make a cut around the perimeter of each chestnut shell and plunge them into boiling water for 1 minute, then peel them.
Step 2Bring 2 cups of water to a boil and add the chestnuts. Reduce the heat to a simmer, cover and cook gently until the pulp is transparent when you cut into a chestnut, 25 to 30 minutes. Overcooking will allow the chestnuts to absorb too much liquid.
Step 3While the chestnuts are still burning hot, force them through a tamis or fine sieve, four to five at a time, collecting the puree in a bowl.
Step 4Mix the puree with a wooden spoon and stir in the sugar. It will melt and dilute the puree. Then add the egg yolks, one at a time, beating the puree vigorously as you go. Stir in the vanilla powder.
Step 5Beat the butter until it is soft and creamy and beat that into the batter.
Step 6Butter a charlotte mold. Heat oven to 350 degrees.
Step 7Whisk the egg whites to firm peaks. Using a spatula, thoroughly mix one-fourth of them into the batter. Spread the remaining whites on top of the batter and then fold them together: Cut into the whole mixture with the spatula, so that you pass under the mass, turning it and placing it over the whites. Turn the bowl and repeat until the batter and whites are thoroughly mixed together. You must do this with large, generous gestures, measured yet swift, going out from the middle to the edges, continually turning the bowl on the table.
Step 8Pour the batter into the charlotte mold. Lightly strike it on a folded towel on the table to compact it.
Step 9Bake until the batter is set enough that a skewer inserted in the center comes out clean, about 1 hour (a springform pan will take 10 or 15 minutes longer). Cool in the pan to ensure that the cake settles before you unmold it. Serve with whipped cream.