Spray a 10x15 inch (25x38 centimeter) jelly-roll pan with baking spray. Line with parchment paper.
Preheat your oven to 350°F (175°C).
In the bowl of a stand mixer, whip the eggs, egg yolk, and sugar on medium-high speed until tripled in volume and mousse-like.
Sift the flour over the whipped eggs in two additions, gently folding after each until mostly incorporated.
Add a spatula full of batter to the cooled melted butter and whisk well. Pour the butter into the batter and fold carefully.
Pour the batter into the prepared jelly-roll pan and spread evenly. Bake for 9 to 11 minutes until lightly browned.
Cover the cake with a damp tea towel to keep moisture in and allow to cool completely.
For the Ganache: Heat the cream to a simmer and pour over chopped chocolate. Whisk to form a ganache and let cool.
For the French Buttercream: Beat the egg yolks, then heat sugar and water to 244F/118C. Slowly pour the syrup into the yolks while mixing.
Whip the mixture until cool, then add the very soft butter and melted milk chocolate.
To assemble: Spread the milk chocolate buttercream on the cooled genoise cake and roll it up using the parchment paper.
Chill the cake to firm up the buttercream, then spread the ganache on the outside.
Dust with powdered sugar to finish.
