Preheat oven to 350°F and line jelly roll pan with parchment paper. Dust a kitchen towel generously with powdered sugar.
Whisk together flour, cocoa powder, baking powder, and salt.
Beat eggs and sugar on high speed for 5 minutes until thick and pale.
Fold in melted chocolate and vanilla until combined.
Gently fold in dry ingredients in three additions.
Spread batter in pan and bake 10-12 minutes until cake springs back when touched.
Immediately flip onto prepared towel, remove parchment, and roll cake with towel from short end. Cool completely.
Beat cream cheese and powdered sugar. Whip heavy cream separately to stiff peaks, then fold together with peppermint extract.
Unroll cake, spread filling leaving 1/2 inch border, sprinkle with candy canes, and roll up without towel.
Place seam-side down, dust with powdered sugar, and garnish with remaining candy canes before serving.