Step 1 To make the ganache, put the milk chocolate and 3 ounces of the bittersweet chocolate in a heatproof bowl. In a medium heavy-bottomed saucepan, stir 6 tablespoons sugar with 2 tablespoons water and the cinnamon stick. Place the mixture over medium-low heat and cook, stirring, until the sugar dissolves. Increase the heat and bring to a boil. Without stirring, boil until the caramel turns a deep amber color, brushing down the sides of the pan with a wet pastry brush to remove any sugar crystals and swirling the pan from time to time. (Depending on the size of your pan, it will take 5 to 7 minutes for the caramel to color properly.) Stand back and add 1 cup plus 2 tablespoons cream and one-fourth teaspoon salt -- the mixture will bubble furiously and it might seize, but it will smooth out as you heat it. With the caramel at a boil, whisk it for another minute, or until it is smooth, then pull the pan from the heat and carefully discard the cinnamon stick.
Step 2 Pour the hot caramel over the chocolate and gently stir until the chocolate is melted and the ganache is smooth. Let stand, stirring occasionally, until it is completely cool, about 1 hour.
Step 3In a stand mixer, preferably with a paddle attachment, or with a hand mixer in a large bowl, beat the butter until smooth and fluffy. Add the chocolate ganache to the butter in four additions, beating on low just until smooth. Scrape the ganache into a container, cover and refrigerate overnight. (The ganache can be made ahead and refrigerated for up to 3 days.)
Step 4Center a rack in the oven and heat the oven to 350 degrees. Butter a 2-inch-high, 8-inch-square pan, dust the inside with flour, tap out the excess and line the bottom of the pan with parchment paper. Put the pan on a baking sheet.
Step 5Sift together the flour, baking powder and the remaining teaspoon salt. Working with a stand mixer, preferably with a paddle attachment, or with a hand mixer in a large bowl, beat the butter at medium speed until smooth and light. Add 1 cup of the brown sugar and beat for about 2 minutes. Add the egg yolks one by one, beating after each addition until well blended. Beat in the vanilla extract, chestnut spread and milk. Reduce the mixer speed to low, add the dry ingredients and gently mix them in. If using a stand mixer, scrape the batter into a large bowl and thoroughly wash and dry the mixer bowl.
Step 6Working in the clean mixer bowl with the whisk attachment or in another large bowl with the hand mixer (and clean beaters), beat the egg whites until they form soft peaks. Add one-fourth cup brown sugar and beat until the peaks are stiff but not dry. Using a large rubber spatula, fold the egg whites into the chestnut batter in three additions. Scrape the batter into the pan.
Step 7Bake for about 50 minutes to an hour, until the cake is golden on top and a thin knife inserted into the center comes out clean. Transfer the cake to a cooling rack an