Step 1Heat the oven to 350 degrees. Butter a 10-inch springform pan with a removable bottom, line it with parchment paper, and set aside.
Step 2Sift together the flour, cocoa, salt and baking soda. In a separate bowl mix together the water, oil and vanilla.
Step 3Beat the eggs in the bowl of an electric mixer, then mix in the sugar. Mix in the water mixture in thirds, alternating with thirds of the sifted dry ingredients, scraping down the sides of the bowl with a rubber spatula between each addition. Mix until smooth.
Step 4Pour the batter into the pan and bake for 20 minutes; reduce the oven temperature to 325 degrees and bake until a toothpick inserted into the middle of the cake comes out clean, 65 to 75 minutes.
Step 5Place the pan on a rack and cool the cake to room temperature. Remove it from the pan and split into 3 equal parts horizontally. Trim the top layer of the cake to make it flat. Place 1 round of cake back into the pan, then prepare the mousse.
Step 1Beat the sugar and yolks in a mixer until pale and thick, about 5 minutes.
Step 2Meanwhile, bring the half-and-half to a boil in a saucepan over medium heat. Pour about 1/2 cup into the yolk mixture, whisking constantly. Return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until the mixture thickens, about 10 minutes.
Step 3Place the chocolate in a large bowl and pour the hot mixture over it. Let stand 1 to 2 minutes, then stir until the chocolate has melted and the mixture is smooth and shiny.
Step 4Whip the cream in another bowl until soft peaks form, about 5 minutes. Fold 1/3 of the cream into the chocolate mixture, then fold in the remaining cream.
Step 5Spread half the mousse onto the bottom cake layer in the pan, then place the middle cake layer on top. Spread the rest of the mousse over it, then place the top cake layer on top. Wrap the cake well in plastic wrap and freeze it overnight.
Step 1Place the chocolate in a bowl. Bring the whipping cream and syrup to a boil in a saucepan, then pour over the chocolate. Let the chocolate melt, about 1 to 2 minutes, then mix to blend completely.
Step 2Remove the frozen cake from the cake pan and place on a rack. Pour 1/2 the glaze over the cake and spread it so that it goes down the sides. Remove the cake from the rack and place on a platter. Refrigerate the cake until the glaze sets, 1 hour. Place the cake back on the rack and pour the remaining glaze over the top. Return the cake to the platter and refrigerate again for the glaze to firm, 1 hour. Let the cake stand at room temperature awhile before serving.