Chestnut flour creates a moist texture with a fine crumb, and chestnut flour makes every layer of this cake taste nutty.This rich, chocolatey cake is best when served the day it is made.
Preheat oven to 350 degrees. Butter two 9-by-2-inch round professional baking pans, and line bottoms with parchment. Butter parchment, and set aside. Using a chestnut knife or a small paring knife, make an incision about 1/8 inch deep through the shell and into the flesh of each chestnut almost all the way around the circumference of the nut. Transfer to a chestnut pan or rimmed baking pan. Roast in the oven until the chestnuts are tender, about 35 minutes. Turn the oven off. Leaving the pan with the chestnuts in the oven, remove several at a time. Working quickly, place 1 chestnut in a towel, and, holding both, peel the chestnut while still hot. Remove and discard the shells and inner skin; set aside. Heat the oven temperature to 325 degrees. Let chestnuts cool completely. Transfer chestnuts to the bowl of a food processor. Add 2 tablespoons sugar, and pulse until very finely ground; set aside.
Place egg whites and cream of tartar in the bowl of an electric mixer fitted with the whisk attachment. Beat until foamy on medium-low speed, 5 to 6 minutes. With mixer running, slowly add 1/2 cup sugar. Raise speed to medium-high; beat until stiff peaks form, 6 to 7 minutes. Transfer egg-white mixture to a bowl.
Into the bowl of an electric mixer fitted with the paddle attachment, sift together the cake flour, chestnut flour, baking powder, cinnamon, salt, and remaining 6 tablespoons sugar. Add the egg yolks and the water, oil, and vanilla, and beat on medium speed until smooth and well combined, about 1 minute.
Using a rubber spatula, carefully and gently fold the flour mixture in 4 or 5 additions into the egg-white mixture until well combined. Gently fold in the reserved chestnuts and chocolate. Evenly divide the batter between the two prepared cake pans, and bake on one shelf, rotating the pans halfway through baking, until golden and a cake tester inserted into the center of the cakes come out clean, about 65 minutes. Transfer to a wire rack until completely cool. Invert pans to remove cakes. Remove the parchment paper.
Place one layer on a cake round or directly onto a cake stand or serving platter. Using an offset spatula, evenly spread the pastry cream on top to within 1/2 inch of the edges. Place the other layer on top.
Pour ganache on top; carefully spread to about 1/4 inch from edges. Ganache will overflow slightly and gently brim edges. Arrange marrons glaces on top of cake, spaced evenly. Set cake aside in a cool place to allow the ganache to firm.