Preheat oven to 375 degrees F. Grease a 15 x 10-inch jelly-roll pan; line with parchment paper. Grease and flour paper.
Beat egg whites in large bowl until soft peaks form; gradually add ½ cup granulated sugar, beating until stiff peaks form.
Beat egg yolks and vanilla in medium bowl on medium speed of mixer 3 minutes. Gradually add remaining ⅓ cup granulated sugar; continue beating 2 additional minutes.
Stir together flour, cocoa, baking powder, baking soda and salt; add to egg yolk mixture alternately with water, beating on low speed just until batter is smooth.
Gradually fold chocolate mixture into beaten egg whites until well blended. Spread batter evenly in prepared pan.
Bake 14 to 16 minutes or until top springs back when touched lightly in center and a toothpick inserted comes out clean.
Allow cake to cool in the pan for ONE minute.
Lift the parchment paper and hot cake out of the pan and onto a flat (heat-safe) surface. Immediately, while the cake is hot, starting at one of the short ends, use your hands to gently and slowly roll the cake (and parchment paper!) all the way up.
Allow the rolled up cake to cool completely, on top of a wire cooling rack. (Setting it on a wire rack allows it to cool underneath the roll, and keeps the cake from sweating).
Transfer to the fridge to cool for an additional 30 minutes.
While the cake roll is cooling in the fridge, mix the cream cheese, butter, powdered sugar and peppermint extract together with an electric mixer until fluffy and smooth.
Gently stir in desired amount of crushed peppermint candies, to taste. Save a handful for sprinkling on the ganache, at the end, if desired.
Once the cake roll is cooled completely, unroll it very carefully. Gently smooth the filling in an even layer over the cake.
Roll up the cake, without the parchment paper. (If you see it start to stick at all to the paper you can use a butter knife gently scrape along the bottom edge of the cake as you roll it up, to help release it.)
Cover with plastic wrap and refrigerate for at least 1 hour.
Heat heavy cream in a saucepan until hot. Pour over chocolate and stir continuously until the chocolate is melted and smooth.
Allow the ganache to cool for several minutes to give it time to thicken up a little.
Gently spoon/pour the chocolate ganache over the top of the peppermint roll. Sprinkle additional chopped peppermint candy on top, if desired.
Refrigerate for at least 20 minutes before serving.
Store in the fridge, covered, for up to three days.