Step 1 Heat the oven to 350 degrees. Lightly butter an 8-inch cake pan and line with parchment. Butter the parchment and flour the pan with cocoa powder, shaking out the excess.
Step 2 Sift together the flour, cocoa, baking soda and powder, and salt. Set aside.
Step 3In a large bowl, beat together the egg and sugar until thickened and lemon-colored, 3 to 5 minutes. Slowly beat in the vegetable oil. Add the dry ingredients and buttermilk in thirds, alternating between each, and scraping down the bowl once or twice. Beat in the coffee and vanilla to form a thin batter and pour into the prepared pan.
Step 4Bake until the cake is set and a toothpick inserted in the center comes out clean, about 40 minutes, rotating the cake halfway though for even baking. Invert the cake onto a cooling rack, peel off the paper and cool completely. Cover the cake completely with plastic wrap and freeze until firm.
Step 5Using a serrated knife, carefully split the firm cake into three thin layers. Using a round cutter, cut 18 circles. The circles can be made up to 1 month in advance; cover tightly and freeze the layers if not using immediately, giving them time to thaw before assembling the final dessert.