Preheat oven to 350°F (180°C). Spray a 14½x9½-inch rimmed baking sheet with baking spray with flour. Line bottom of pan with parchment paper; spray parchment.

In the bowl of a stand mixer fitted with the whisk attachment, beat eggs at medium-high speed until foamy. Gradually add sugar, beating until mixture is thick, pale yellow, and doubled in size, about 5 minutes. Beat in vanilla.

In a medium bowl, whisk together flour, cocoa, baking powder, and salt. Using a balloon whisk, gently fold flour mixture into egg mixture. Spread batter into prepared pan.

Bake until cake springs back when lightly pressed in center, 9 to 11 minutes. (Do not overbake.)

Meanwhile, sift cocoa into a 15x10-inch rectangle onto a clean kitchen towel.

Immediately run a thin knife or a small offset spatula around edges of cake to loosen. Invert cake onto cocoa on towel; gently peel off parchment. Sift cocoa onto cake. Starting at one short side, gently roll up cake and towel together, and place, seam side down, on a wire rack. Let cool completely.

Carefully unroll cooled cake. Transfer 1 cup (170 grams) Peppermint Cream Filling to a pastry bag fitted with a large petal piping tip (Wilton No. 125); spread remaining filling onto cake, leaving a ½-inch border on one short side. Sprinkle chopped bark onto filling. Gently reroll cake and filling without towel. Carefully transfer cake to a baking sheet, and refrigerate until set, about 20 minutes, or until ready to serve.

Just before serving, trim edges of cake roll, if desired. Pipe reserved filling on top of cake roll; garnish with peppermint bark, if desired. Refrigerate in an airtight container for up to 3 days.