Preheat an oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch cake pan or line it with parchment paper.

Sift the flour and cocoa powder together and set aside. Combine the eggs and 3/4 cup sugar in a mixing bowl and beat until very thick, about three minutes. Use a spatula to carefully fold in the flour mixture. Gently scoop the batter into the prepared pan and bake until the top springs back when lightly pressed and a toothpick inserted in the center comes out clean, 25 to 30 minutes. Cool the cake in the pan for 10 minutes before removing to cool completely on a wire rack.

To make the simple syrup, bring 1/2 cup water and 3/4 cup sugar to a boil in a saucepan over medium-high heat. Remove the pan from the heat and set aside.

To make the Italian meringue, combine 1/4 cup water with the 7/8 cup of sugar in a saucepan. Bring the mixture to a boil, stirring to dissolve the sugar (don't stir once the mixture begins to boil). Use a candy thermometer and bring the sugar to the soft ball stage (240 degrees F/115 degrees C). While the sugar is boiling, beat the egg whites with an electric mixer on medium-low speed until soft peaks form.

When the boiling sugar syrup has nearly reached soft ball stage, increase the mixing speed for the egg whites to high. Carefully pour the hot sugar syrup into the egg whites between the beaters and the side of the bowl. Continue beating on high speed until the meringue has cooled to room temperature.

Melt the bittersweet chocolate in the top of a double boiler over just-barely simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching, just until melted. Remove from heat and allow to cool until the chocolate is room temperature but still fluid.

Whip the 1 3/4 cups cream until medium-stiff peaks form.

Use a rubber spatula to fold the melted chocolate into the egg white meringue. Add 1/3 cup of room-temperature cream and mix gently until blended. Fold 1/3 of the whipped cream into the chocolate meringue mixture to lighten it; then gently fold in the remaining 2/3 of the whipped cream.

To assemble the cake, split the sponge cake into two layers. Set one cake layer on a turntable or plate. Brush the cake well with the simple syrup. The cake will literally act as a sponge and absorb the syrup, which will keep it from being dry. Spread 1/3 of the chocolate cream on the cake, and top it with the second cake layer. Repeat with the syrup and the cream. Spread the remaining chocolate cream on the sides of the cake. Refrigerate until serving.