Grease a 9- by 13-inch jelly roll pan, and line with parchment paper.
In a medium bowl, sift together cake flour, cocoa powder and salt.
In a medium heatproof bowl, combine 1/2 cup sugar, eggs and egg yolks. Place bowl over a water bath and cook, stirring constantly, until sugar has dissolved.
Preheat oven to 450 degrees.
Place the egg and sugar mixture in the bowl of a stand mixer and whisk well, until mixture is thick and light in color, about 6 minutes. Add flour and cocoa powder mixture and gently fold to combine. Fold in butter, vanilla and peppermint schnapps. Spread evenly in prepared pan. Bake for 6 minutes.
In a medium heatproof bowl, heat egg whites and 1 cup sugar over a water bath until sugar is dissolved.
Beat the cooked egg white mixture in a stand mixer bowl with a whisk attachment. Whisk for about 10 minutes, until lofty and pale in color. The meringue will hold stiff peaks when ready. Switch to the paddle attachment and slowly add butter a few tablespoons at a time until all butter is incorporated. Add salt and peppermint schnapps. Split the frosting in half and tint half of it with red food coloring.
Place the red frosting into a piping bag and the white frosting into a separate piping bag. Pipe stripes over the top of the jelly roll cake and roll it up. Refrigerate for about an hour. Insert pop sticks into the cake, then slice. Freeze each slice for about 30 minutes until firm. Dip the exterior edge of the cake in dark chocolate and sprinkle with crushed candy canes. Allow to set, then serve!