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

Ingredients

• 500 grams (2 1/2 cups) granulated sugar
• 250 grams egg whites (from about 8 large eggs)
• 1 tablespoon lemon juice
• Pinch of salt
• 750 grams (3 1/3 cups) unsalted butter, at room temperature and cut into cubes
• 1 tablespoon vanilla extract
• 95 grams egg yolks (from about 5 large eggs)
• 95 grams (a scant 1/2 cup) granulated sugar
• 4 vanilla beans, split and scraped
• 25 grams (5 teaspoons) water
• 450 grams whipped cream (a scant 2 cups heavy cream before whipping)
• 400 grams (about 1 1/4 cups) white chocolate couverture pistoles or callets
• 400 grams (2 cups) granulated sugar
• 400 grams (1 2/3 cups) water
• Two 9-inch rounds vanilla cake, such as Basic Vanilla Cake, recipe follows
• 2 sticks unsalted butter, at room temperature, plus more for the pans
• 3 cups all-purpose flour, plus more for the pans
• 1 tablespoon baking powder
• 1/2 teaspoon salt
• 1 1/2 cups sugar
• 4 large eggs, at room temperature
• 3/4 cup heavy cream