Preheat the oven to 350 degrees. Oil a 9-inch springform cake pan with butter or coconut oil.
In a blender or food processor, pulse the chestnuts, coconut milk, and vanilla extract until you have a coarse paste.
Break the dark chocolate into pieces and place it in a small saucepan. Add the butter and warm over low heat, stirring frequently, until the butter and chocolate are melted and smooth. Remove from heat.
Separate the eggs, placing the yolks in a large mixing bowl and the whites in another large mixing bowl. Whisk the maple syrup into the egg yolks until well blended, then stir in the chestnut puree and the melted chocolate.
Beat the egg whites to stiff peaks and then fold them into the chocolate batter in thirds. When the egg whites are just incorporated, spoon the batter into the prepared pan. Bake for 35 minutes, or until the cake is only slightly jiggly in the center when you move the pan. Cool completely before slicing. If you want to dust the top with cocoa, spoon a couple of tablespoons of cocoa powder into a fine sieve and shake it gently over the top of the cake. If you don't want a big mess, place the cake on some waxed paper before you do this step.
