1 Preheat oven to 450F. Position a baking rack in the center of the oven.
2 Prepare the baking sheet: Spray a 13 x 17-inch rimmed baking sheet with cooking spray, line bottom with parchment paper, then spray again and dust with cocoa powder, tapping out any excess. Set aside.
3 Sift together the flour, cocoa powder, and salt for the cake. Set aside.
4 Warm the eggs and sugar: Make a double boiler by filling a medium saucepan with 2 inches of water, and brining the water to a gentle simmer over medium heat. Combine the eggs, sugar, and vanilla extract in the bowl of a stand mixer, or another large heatproof bowl, and set this bowl over the simmering water. The bowl should be larger than the pan and sit above the surface of the simmering water.
Begin whisking the eggs, sugar, and vanilla extract with a sturdy whisk. Continue whisking until the sugar has dissolved and the egg mixture is pale and warm to the touch. Remove from heat.
5 Beat the egg mixture until tripled in volume: Using a stand mixer with a whisk attachment or a hand mixer, beat egg mixture on high speed until mixture is very pale , has a shiny gloss, and has nearly tripled in volume. This will take 5 to 10 minutes depending your mixer.
6 Fold the flour and cocoa mixture into the egg mixture in two batches: Sprinkle half of the flour and cocoa mixture over the surface of the eggs, and gently fold until just barely combined. Sprinkle the remaining flour and cocoa mixture over the top and fold until you see no more dry streaks and the mixture looks uniform.
7 Drizzle the melted, cooled butter into the batter. Stir to combine.
8 Working quickly, spoon mixture out onto prepared baking sheet. Use an offset spatula to spread batter out evenly.
9 Bake for 6 to 7 minutes, or until cake has pulled away from sides and is springy to the touch. Cool cake 2 for 3 minutes, but no longer.
10 While the cake is baking, prepare the kitchen towel for rolling: Find a clean kitchen towel that is larger than your baking sheet (or use two, overlapping). Dust it all over with cocoa powder.
11 Roll the cake in the kitchen towel: With swift, confident motions, run a knife along the outside edge of the cake pan. Set the pan on its side, and then flip face down onto the dusted towel. Carefully lift the pan up and away, and peel away parchment.
Fold an edge of towel over one of the shorter sides of the cake, and gently roll the cake up. Set rolled cake on a wire rack and cool completely, an hour or longer.
12 Make the whipped cream filling: Whip the heavy cream until is billowy, then add the sugar and peppermint extract. Continue whipping until the cream just barely holds firm peaks; be careful not to overwhip.
13 Fill the cake with whipped cream: Gently unroll cake on a clean surface. Spread the whipped cream filling evenly over the cake, leaving a 1-inch border on all sides. Roll the cake back up again (this time without the towel!). If any whipped cream squeezes out as you roll, spoon it up and add it back in.
14 Chill the cake: Wrap cake roll in parchment, then plastic wrap, and set in fridge to chill at least 30 minutes to set, or as long as overnight.
15 When ready to finish the cake, make the ganache: Make a double boiler by filling a medium saucepan with 2 inches of water, and bringing the water to a gentle simmer over medium heat. Set a larger bowl on top of the saucepan, over the water.
Add the heavy cream, two-thirds of the chopped chocolate, and a pinch salt to the bowl. Stir until melted. Remove the bowl from heat, and stir in remaining chocolate and corn syrup.
16 Drizzle the cake with ganache: Unwrap the chilled cake and set it on a platter seem-side down. Slip two pieces of parchment on either side of the "log" to catch the drips. Drizzle the prepared ganache over roll until roll is completely covered. Remove the parchment paper "drip catchers." Scatter the peppermint candy bits on the top.
17 Chill and serve: Set the cake in the fridge and chill 20 minutes. Slice and serve!