Preheat the oven to 350°F. Separate the eggs, reserving the whites. Add the egg yolks and sugar to the bowl of a stand mixer. Beat with a paddle attachment until the egg yolks are pale yellow and thick. Add the chestnut purée and vanilla and beat until combined. Add the melted butter and beat until combined.
In a separate bowl whisk together the flour, cocoa powder, baking powder, and salt. Add the dry ingredients alternating with the milk to the mixer, beating between each addition just until combined. Do not overmix.
In a clean bowl, beat the egg whites until stiff peaks. Gently fold the stiff egg whites into the batter in three batches. Pour the batter evenly into a lightly greased bundt pan.
Bake for 50 to 60 minutes until a skewer inserted into the middle comes out clean. Transfer to a rack and let cool for 5 minutes. Invert cake onto a serving platter and remove the pan. Allow the cake to cool to room temperature before topping with the ganache.
Candied Chestnuts
Have a piece of parchment paper ready for the chestnuts. Melt the butter in a non-stick skillet over medium heat. Add the chopped chestnuts along with the sugar, stirring together. Cook the chestnuts, tossing the pan regularly, until the sugar melts and begins to caramelize, about 3 to 4 minutes.
Once the melted sugar has darkened into a caramel colour, transfer them to the parchment paper. Spread the chestnuts out and allow to cool.
Chocolate Ganache
Finely chop the chocolate and transfer to a mixing bowl. Heat the cream over high heat just until it begins to boil. Immediately pour the hot cream over the chocolate. Add the vanilla and optional rum. Let the chocolate sit for 3 to 4 minutes to allow it to melt.
Whisk the chocolate and cream together until smooth and glossy. If the ganache is too runny, allow it to cool before pouring over the cake. The ganache will harden as it cools. If it hardens before you have poured it over the cake, warm it up slightly.
Pour the chocolate ganache evenly over the bundt cake. Top the cake with pieces of candied chestnut to garnish. Allow the ganache to set before serving and enjoy!