For cake: Preheat oven to 350°F Butter and flour 9x2-inch round metal baking pan. Line bottom of pan with parchment paper.
Put chestnut spread in small bowl. Mix in 3 tablespoons sugar, 2 teaspoons vanilla extract and 2 teaspoons cinnamon. Set aside.
Sift flour, baking powder, and salt into medium bowl.
Using electric mixer, beat butter in large bowl until fluffy. Beat in 1 cup brown sugar, then egg yolks and vanilla extract. Beat in chestnut spread mixture, then milk. Mixture will look a bit grainy.
Sift dry ingredients over the mixture and gently mix together by hand.
Using clean dry beaters, beat egg whites in another large bowl until soft peaks form. Add remaining 1/4 cup brown sugar and beat until stiff but not dry. Fold egg whites into batter in 3 additions.
Transfer batter to prepared pan. Bake cake until golden and tester inserted into center comes out clean, about 50 to 60 minutes. Cut around cake to loosen. Cool cake completely in pan on rack.
For Chestnut Cream: Melt chocolate over simmering water or in microwave. Set aside to cool. Place one cup unsweetened chestnut spread in bowl of food processor (mini bowl is fine). Pulse a few times to loosen. Add powdered sugar, vanilla extract and process to combine well. Add melted chocolate and process to combine well.
In large bowl of electric mixer (preferably chilled) whip the cream on high until until very soft peaks form. Add the chocolate chestnut mixture and beat until stiff peaks form.
For Dark Chocolate Ganache: Place the semisweet chocolate in a 3-quart stainless steel bowl. Heat the heavy cream and the butter in a saucepan over medium high heat. Bring to a boil. Pour the boiling cream over the chocolate and allow to stand for 5 minutes. Add the vanilla, the coffee, the liquor and the salt. Stir until smooth. This may take a few minutes as the cream absorbs the chocolate. Once well combined, set aside to cool. If desired, set aside and chill about 1 1/2 cups ganache to pipe onto finished cake.
For Chestnut Brandy Syrup: Mix all ingredients in a small bowl until sugar dissolves.
Assemble the cake: Take the cake out of the pan and remove parchment. Split into three even layers. Arrange one of the cake layers in a 9-inch springform pan. Brush with the chestnut brandy syrup. Evenly spread half the filling over the cake and top with the second layer. (It's best to use an offset spatula to spread the filling). Brush layer with the with syrup. Remove ring from springform pan and coat sides and top with room temperature ganache. You will have some ganache left over which you can use for something else like chocolate truffles. Decorate with whole chestnuts, colored sugar and chopped chestnuts. If piping chilled ganache, place it in a pastry bag and pipe a decorative design onto cake.
Cut cake with a serrated knife, wiping the blade clean after each slice.
1) If you can find sweetened chestnut cream with vanilla use one cup in cake instead of sweetening it as indicated.
2) If you can't find chestnut cream you can make your own with jarred chestnuts, or roast your own.
3) If you can't find chestnut liquor, use brandy, rum, or spiced rum.