This festive yule log is made from a red-velvet cake filled with fluffy peppermint frosting.
Preheat oven to 400 degrees. Butter and line a 12-by-17-inch jelly-roll pan with parchment paper. Butter and lightly flour parchment; set aside. Lay a kitchen towel on top of a wire rack, and dust with confectioners' sugar; set aside.
Put egg yolks into the bowl of an electric mixer fitted with the whisk attachment; beat on high speed until pale, 4 to 5 minutes. Transfer to a medium bowl; set aside.
Put egg whites into the clean bowl of the electric mixer fitted with the clean whisk attachment; beat on medium speed until soft peaks form, about 2 minutes. Raise speed to medium-high. Gradually add granulated sugar; beat until stiff peaks form. Gently whisk in food coloring. Transfer egg-white mixture to a large bowl.
Fold beaten egg yolks into egg-white mixture. Sift cocoa powder and flour over top, and gently fold in. Pour into prepared pan, smoothing top with an offset spatula.
Bake until cake springs back when touched, 10 to 11 minutes. Run an offset spatula or sharp knife around sides of pan; invert onto prepared towel. Remove parchment. Dust with confectioners' sugar.
Starting at short end closest to you, roll cake in kitchen towel. Let cool completely, seam side down, on rack.
Unroll cake. Using an offset spatula, spread with 2 cups Peppermint Frosting, leaving a 1/4-inch border on all sides. Starting at the short end closest to you, reroll cake (do not include towel this time). Transfer, seam side down, to a serving platter. Spread with remaining frosting. Sprinkle with crushed candy. Cake can be stored up to 5 hours at room temperature.