16 tablespoons (2 sticks) unsalted butter, at room temperature
2 cups sugar
2 1/2 cups all-purpose flour
2 teaspoons baking powder
4 large eggs
3 egg yolks
1/2 cup buttermilk
1 tablespoon grated lemon zest
1 tablespoon strained lemon juice
1 teaspoon vanilla extract
1/2 cup water
1/2 cup sugar
1/3 cup lemon juice
2 teaspoons vanilla extract