Preheat oven to 350°. Prepare three 6-inch cake pans by spraying with pan spray and lining bottom with parchment paper. Set up a double boiler. (The water should be simmering, and keep it handy—you’ll use it again for the mascarpone mousse.)
In a medium bowl, combine flour, salt, and 1/4 cup sugar. In a small bowl, combine butter and vanilla.
Place eggs, yolk, and 1/2 cup sugar in the bowl of a stand mixer. Place over the double boiler, whisking constantly until mixture is warm (no more than 110°) and sugar is dissolved, about 5 minutes. Place bowl on stand mixer with a whisk attachment and whip on high for 10 minutes. The mixture should be fluffy and have tripled in volume.
Add 3/4 of egg mixture to flour. Using a rubber spatula, gently fold flour into eggs until mixture is well incorporated. Add butter mixture and the remaining fluffy eggs to cake batter. Gently fold to combine.
Portion batter between your cake pans; each pan should be filled half full with batter. Bake until golden brown, about 20 minutes. Cool completely before cutting into 1- by 1-inch cubes for assembly.