Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. In a large mixing bowl, whisk egg whites and cream of tartar until stiff peaks form, about 3 to 5 minutes. Gradually fold in flour, cornstarch, baking powder, salt, sugar, peppermint extract, and food coloring until just combined.

Transfer the mixed batter into a piping bag with a round tip. Pipe alternating stripes of white and red batter on the baking sheet to create a candy cane pattern, ensuring smooth edges.

Bake in the preheated oven for about 10 to 12 minutes until the cake springs back when pressed. It should be lightly golden.

Remove the cake from the oven. While warm, flip it onto a clean towel dusted with confectioners' sugar. Peel off the parchment and roll the cake with the towel to form a spiral. Cool completely in this shape.

In a medium bowl, beat softened butter and cream cheese with an electric mixer until smooth. Gradually add confectioners’ sugar, peppermint extract, and salt, mixing until fluffy. Set aside.

Once the cake is cool, unroll it and spread the cream cheese frosting evenly on top. Reroll the cake without the towel for a filled cake roll.

Transfer the roll to a platter and frost the exterior with remaining frosting. Sprinkle crushed candy canes on top.

Refrigerate the roll for at least an hour before slicing and serving.