Spray a 10x15 jelly roll pan with nonstick spray, line it with parchment, and spray the parchment as well. This ensures the cake releases easily. Preheat your oven to 350°F.
Double-sift the cake flour, cocoa powder, and baking powder into a medium bowl. Melt the butter and set it aside to cool slightly.
Whisk the eggs and granulated sugar in a large heatproof bowl (the stand mixer bowl works great). Set the bowl over simmering water and whisk until the sugar dissolves, about 4–5 minutes. Transfer the bowl to the stand mixer and beat on high speed for 3 minutes, until the mixture triples in volume and forms thick ribbons. Stir in the vanilla and peppermint extracts.
Gently fold in the sifted dry ingredients in quarters, being careful not to deflate the batter. Along with the final addition or dry ingredients pour the melted butter down the side of the bowl and fold gently to incorporate. Do not over mix, you don't want to deflate the batter.
Spread the batter evenly into the prepared pan, tapping it gently to release air bubbles. Bake for 15 minutes or until the center springs back when touched. Be careful not to overbake, as this can cause cracks.
Dust a clean tea towel generously with confectioners’ sugar. While the cake is still warm, turn it out onto the towel, remove the parchment, and dust the top with more sugar. Starting at a short edge, roll the cake tightly into the towel and let it cool seam-side down on a wire rack for about an hour.