For the cookie cake: Preheat the oven to 350 degrees F. Grease an 8-inch cake pan with nonstick cooking spray and line it with parchment. Set aside.
In a large bowl, combine the almond and hazelnut flours, brown and granulated sugars, salt and baking soda. In a small bowl, combine the vanilla and almond extracts and egg. Add the wet ingredients to the dry ingredients, add the chocolate chips and stir to combine. It may seem dry at first but keep on stirring. Pat the dough out evenly in the prepared cake pan.
Bake until golden brown on top; begin checking for doneness at 22 minutes. Let the cake cool fully in the pan.
For the buttercream: In a stand mixer fitted with a paddle attachment, beat together the powdered sugar, butter, vanilla and salt. Once combined, beat in the heavy cream until smooth.
Remove the cake from the pan. Transfer the buttercream to a piping bag and decorate the cake as desired (or spread on the cake to decorate).