Prepare the sponge cake first. Preheat the oven to 350F/177C. Line the bottom of a 6-inch/15-cm round cake pan with parchment paper; don't grease the sides. Place the eggs and sugar into a stand mixer bowl and whisk on high speed for 5 to 6 minutes, until the eggs are voluminous and pale in color. In a separate bowl, combine the flour and baking powder. Sift the dry ingredients into the eggs in small batches, folding gently but thoroughly. Pour in the butter last and fold in gently.
Pour the cake batter into the prepared pan and bake in preheated oven for 25 to 28 minutes, until the center is set and the top golden brown. Remove the cake from the oven and run a knife along the edge of the pan to release the cake from the sides. Allow the cake to cool completely, then split the layer into 3 or 4 layers.
Next, prepare the gelee layer. Line the bottom and sides of a 6-inch/15-cm round pan with plastic wrap, creating a leak-proof seal. Pour the pomegranate juice into a small saucepan and add the sugar and agar gelatin. Cook the mixture over medium-high heat until the mixture comes to a simmer. Boil for about 30 seconds, then remove from heat. The mixture will start to thicken as it cooks.
Pour the pomegranate mixture into the prepared pan, then carefully transfer into the refrigerator. The layer will set up in approximately 20 minutes. Once the gelee is set, use the plastic to remove the layer from the pan.
Prepare an 8 or 9-inch (20-23cm) spring form pan to be used for assembling the cake. Line the sides with plastic wrap or an acetate cake collar; this will make it easier to remove the cake from the pan. Assemble the center first. Use a sponge cake layer as the first and second layer; soak each sponge cake layer generously with pomegranate liqueur using a pastry brush. Top with the gelee, then add the additional one or two cake layers.
Next, prepare the chocolate mousse. In a large bowl, cream together the softened butter, sweetened condensed milk, melted chocolate, cocoa powder and vanilla extract. Mix for 2 to 3 minutes, until the mixture is smooth; set aside.
Place the egg whites into a stand mixer bowl and whisk for 2 to 3 minutes until soft peaks form; set aside. Pour the water and agar gelatin into a small saucepan. Cook the mixture over medium heat until it begins to simmer and thicken, about 3 minutes. Begin adding the sugar, 1/2 cup at a time, and mix the sugar into syrup after each addition. Once all the sugar is added, continue cooking the syrup and bring it to a boil; boil for 2 minutes.
Set the mixer with the egg whites to medium speed and pour the hot syrup in a slow and steady stream into the egg whites, avoiding the whisk attachment. Once all the syrup is added, turn the mixer to high speed. Mix on high speed for 6 to 7 minutes, until the meringue begins to thicken and cool. Add the chocolate mixture and lemon juice, then mix again for 2 minutes.
Pour the chocolate mousse over the assembled center cake and along the sides. Work quickly as the mousse will begin to set quickly. Use an off-set spatula to level off the top. Set the mousse cake into the refrigerator to set and chill for 1 hour. Once the cake is set and chilled, carefully remove it from the spring form pan and place the cake onto a wire rack arranged over a baking tray to catch any extra glaze.
Prepare the glaze: combine the chocolate, milk and shortening in large measuring cup. Microwave the chocolate in 30 second intervals and stir well until mixture is completely smooth and clump-free. Allow the chocolate glaze to cool for 5 to 7 minutes, then pour over the cake. Use a flat spatula to spread the chocolate evenly over the top and sides.
Garnish the top of the cake with melted white chocolate and pomegranate arils and pieces. Keep cake refrigerated.