Preheat your oven to 350°F (180°C). Line a 9-inch (22 cm) cake pan with parchment paper.
In a bowl, whisk together the whole wheat flour, baking powder, cocoa powder, and cane sugar.
In a separate bowl, combine the coconut milk, coconut oil, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined. Be careful not to overmix.
Pour the batter into the prepared cake pan and bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean. Let the cake cool completely in the pan before frosting.
Prepare the chestnut cream: in a bowl, combine the chestnut puree, erythritol, and a splash of coconut milk until smooth and creamy.
Using a long serrated knife, slice the cooled cake horizontally in half. Spread half of the chestnut cream evenly over the bottom layer.
Place the top layer of the cake on top of the cream. Frost the top and sides of the cake with the remaining chestnut cream.
Dust the cake with cocoa powder and decorate with chestnut pieces.
Refrigerate the cake for at least 1 hour before serving to allow the flavors to meld.
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