Whisk together the flour, cornstarch, cocoa powder, baking powder, and salt in a small bowl. Set aside.

Separate the eggs, placing whites in one large mixing bowl and yolks in another.

Beat the egg whites on medium-high speed until foamy. Gradually add ½ cup of sugar while continuing to beat. Increase speed to high and beat just until stiff peaks form. Set aside.

Beat the egg yolks with the remaining ¼ cup sugar and vanilla extract until the mixture thickens and becomes pale, approximately 3 minutes.

On low speed, beat the flour mixture into the yolk mixture until just combined. Stir in one-quarter of the beaten egg whites to lighten the batter. Gently fold in the remaining whites until no white streaks remain.

Spread the batter evenly in the prepared pan, smoothing the top with a spatula.

Bake for 12 to 14 minutes, until the top springs back when gently pressed. Cool on a wire rack for 2 minutes only.

Dust a clean kitchen towel generously with confectioners' sugar. Loosen the edges of the cake from the pan and invert it onto the prepared towel. Remove the pan and carefully peel off the parchment paper.

Starting from a short end, roll the cake up in the towel. Place seam-side down on the wire rack and allow to cool completely.

While the cake cools, place the ice cream on the counter to soften until spreadable but not melted.

Unroll the cooled cake carefully. Spread the softened ice cream evenly over the entire surface of the cake.

Roll the cake back up without the towel. Wrap tightly in parchment paper, then wrap again in aluminum foil. Place seam-side down in the freezer and freeze overnight until completely firm.

When ready to glaze, combine the heavy cream, chopped chocolate, and corn syrup in a small saucepan. Heat over low heat, stirring constantly, until the chocolate melts completely and the mixture becomes smooth and glossy, 1 to 2 minutes. Remove from heat and stir in the vanilla extract. Cool to room temperature.

Unwrap the frozen cake roll and trim both ends for a clean appearance. Place the roll on a wire rack set over a baking sheet or parchment paper.

Pour the cooled glaze along the top of the cake roll, using a spatula to spread it and encourage it to drip down the sides for complete coverage.

Immediately sprinkle crushed candy canes over the glazed cake, pressing gently to adhere.

Return the cake to the freezer uncovered until the glaze firms up, approximately 1 hour.

To serve, use a serrated knife warmed under hot water and dried between cuts. Slice into portions and serve immediately on chilled plates.