To Make the Cake: Preheat the oven to 350°. Place the rack in the center of the oven. Butter and flour a 10-inch cake pan that is 3 inches deep such as a springform mold.
Sift the 1/2 cup flour, the cocoa, and the salt together onto a sheet of parchment paper and set aside. In the bowl of a stand mixer fitted with the whisk attachment, beat the eggs, sugar, and vanilla at high speed until the mixture has tripled in volume and is very thick, about 8 minutes. When the whisk is lifted, the batter will form a thick ribbon as it falls back into the bowl.
Lower the speed to stir and carefully tap the dry ingredients into the egg mixture. As soon as all the flour has been added to the eggs, stop the machine. Pour in the melted butter, making sure to leave the white, milky solids behind. With a large rubber spatula, using as few strokes as possible, finish folding the flour mixture and butter into the batter until evenly mixed.
Immediately scrape the batter into the prepared pan, place the pan on a baking sheet, and bake until the cake feels just firm to the touch, about 40 minutes. Transfer the cake to a rack and let it cool for about 5 minutes. Then turn the cake upside down onto a rack to cool. This will flatten the slightly domed top.
To Make the Syrup: Place the sugar and 1/2 cup water in a small saucepan over medium-high heat. Bring the mixture to a boil while stirring to dissolve the sugar. Add the kirsch and remove from the heat. Pour the syrup into a small cup or bowl and set it aside.
To Assemble the Cake: In a large bowl, whip the cream with the sugar and vanilla on medium-high speed until it holds firm peaks. Do not overbeat; the whipped cream should be smooth and firm. Divide the cream into 4 equal portions and set them aside. (This helps prevent getting to the last bit of decorating and discovering you have run out of cream.) Drain the cherries and divide them into 2 equal piles. Reserve 8 to 12 cherries to garnish the top of the cake if you do not have fresh cherries.
Place the cake on a work surface with its original top up. Trim off any hard crusts. With a long serrated knife, cut the cake horizontally into 3 even layers. Transfer the top layer to a serving plate, arranging it top side down. Brush it liberally with the syrup. With an offset spatula or rubber spatula, smooth on a 1/2-inch layer of whipped cream. Push the cream a little beyond the edge of the cake. (This prevents gaps when you settle the next layer on top.) Nestle half of the cherries into the whipped cream, scattering them evenly over the top.
Place the middle cake layer on top of the cherries, pressing it lightly into the whipped-cream layer. Brush with syrup, spread with whipped cream, and scatter the remaining half of the cherries over the cream.
Finally, add the last cake layer, cut side up, on top of the cherries, again settling it into the whipped-cream layer. Brush with syrup. With an icing spatula or a large rubber spatula, spread a thin layer of whipped cream over the top of the cake. Spread a thicker layer onto the sides.
Pastry shops add a decorative scalloped edge of ground dark chocolate around the base of the cake. Fill your cupped palm with some of the ground chocolate and lift and tilt it onto the base of the cake all around the bottom edge. Rotate the cake between handfulls. Its the heel of your hand that forms the scalloped edge.
Rotate the edge of a sharp knife against the block of chocolate to make curls or cut shavings with a vegetable peeler. Pile them on top of the cake.
Scoop the remaining whipped cream into a pastry bag fitted with a medium star tip. Pipe fat rosettes all around the top edge of the cake. Press a fresh or spirited cherry into the center of each rosette. Refrigerate the cake for at least 4 hours to let the flavors meld. Just before serving, dust the top with powdered sugar.
Alcohol-Free Variation Use about 24 ounces of preserved sour cherries in syrup. Drain the cherries, reserving the syrup and cherries separately. In a small saucepan, bring to a boil 1/3 cup espresso or strong coffee, the reserved syrup, and 3/4 cup sugar (or to taste), stirring until the sugar dissolves. Remove from the heat and reserve until needed.
Bûche de Noël de Henri Variation For our Christmas menu in 2010, we used Black Forest flavors for our bûche de Noël. We baked the génoise as a sheet cake, soaked it with the kirsch syrup, spread it thickly with the whipped cream, and then scattered the cherries over the cream before rolling up the cake. We iced it with the traditional chocolate buttercream. This makes a lighter-than-usual bûche, and our guests cleaned their plates.
Notes: If using jarred cherries, drain them, reserving both the syrup and the cherries. Measure the amount of syrup and set aside. Macerate the cherries in a glass bowl in 1/2 cup of kirsch for 1 hour, tossing them occasionally. Drain the cherries, reserving them and the kirsch separately. Pour the syrup into a small saucepan with the kirsch and add sugar, if needed, to make a slightly sweet, cherry-flavored syrup. Bring to a boil over high heat, stirring until the sugar dissolves. Remove from the heat and set aside until needed. You need about 1 cup of syrup for the cake. Use the rest as a sauce for ice cream.