Preheat oven to 375°F. Grease and line a 15×10-inch jelly-roll pan with parchment paper, then grease and flour the paper. Beat egg whites until soft peaks form. Gradually add 1/2 cup sugar until stiff peaks form. In another bowl, beat egg yolks with vanilla for 3 minutes, add 1/3 cup sugar, and beat another 2 minutes. Combine flour, cocoa, baking powder, baking soda, and salt. Add to yolk mixture alternately with water. Fold the chocolate mixture into egg whites until smooth. Spread the batter in the prepared pan and bake 14–16 minutes until it springs back when touched. Let cool 1 minute, then roll the warm cake with parchment and cool completely. Chill rolled cake for 30 minutes. For the filling, beat cream cheese, butter, powdered sugar, and peppermint extract until smooth. Stir in crushed candies. Unroll cake, spread filling evenly, leaving a 1/2-inch border, then roll it back up (without parchment). Wrap and chill for at least 1 hour. For ganache, heat cream until hot, pour over chocolate chips, stir until smooth. Cool slightly, then pour over cake. Top with crushed peppermint and chill at least 20 minutes before serving.