Vanilla Bean Buttercream, Vanilla Bean White Chocolate Mousse and Vanilla Syrup for Wedding Cake

1. For the buttercream: Combine the sugar and egg whites in a double boiler and heat to 120 degrees F.
2. Transfer the egg white mixture to a stand mixer fitted with a whisk attachment. Add the lemon juice and salt and beat on high speed until completely cooled, about 15 minutes. Add the butter piece by piece and whip until light fluffy, about 10 minutes. Fill a pastry bag fitted with a round tip and reserve the rest. 
3. For the vanilla bean white chocolate mousse: Whip the egg yolks on high speed in the bowl of a stand mixer fitted with a whisk attachment until light and foamy, 3 to 4 minutes. Heat the sugar, vanilla bean paste and water to 120 degrees C in a small pot over medium-high heat. Add the sugar syrup to the whipping yolks and beat until cool, about 15 minutes. Once cooled, fold in the whipped cream. 
4. Melt the white chocolate over a double boiler until 110 degrees F., about 10 minutes. Add the melted chocolate to the egg and cream mixture and fold to combine. Fill a pastry bag fitted with a round tip and reserve the rest.
5. For the vanilla syrup: Combine the vanilla bean paste, sugar and water in a small saucepan over medium-high heat until the sugar is dissolved. Cool completely.
6. To assemble the cake: Split the cake rounds in half to make 4 layers. Brush the top of each with 3 tablespoons of the vanilla syrup. Place 1 round on desired platter and pipe the buttercream around the top edge of the cake to create a dam. Fill the dam with a layer of the white chocolate mousse. Top with a second cake round and repeat piping and filling with the remaining layers, leaving the top undecorated. Place the stack in the freezer until firm, 30 minutes to 1 hour. 
7. Remove from the freezer and lightly frost the whole cake with some of the buttercream. Place the cake back in the freezer to firm up, another 30 minutes to 1 hour. Frost and decorate the cake as desired with the remaining buttercream and mousse.

Basic Vanilla Cake:

1. Preheat the oven to 350 degrees F. Butter two 9-inch-round cake pans and line the bottoms with parchment paper; butter the parchment and dust the pans with flour, tapping out the excess.
2. Whisk 3 cups flour, the baking powder and salt in a bowl until combined. Beat 2 sticks butter and the sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Reduce the mixer speed to medium; beat in the eggs, one at a time, scraping down the bowl as needed. Beat in the vanilla. (The mixture may look separated at this point.)
3. Mix 1/2 cup water with the cream in a liquid measuring cup or bowl. Beat the flour mixture into the butter mixture in 3 batches, alternating with the cream mixture, beginning and ending with flour, until just smooth.
4. Divide the batter between the prepared pans. Bake until the cakes are lightly golden on top and the centers spring back when pressed, 25 to 30 minutes. Transfer to racks and let cool 10 minutes, then run a knife around the edge of the pans and turn the cakes out onto the racks to cool completely. Remove the parchment. Trim the tops of the cakes with a long serrated knife to make them level, if desired.