14 tablespoons unsalted butter, melted, plus more for pan
3 3/4 cups flour, plus more for pan
2 cups sugar
2 tablespoons baking powder
3/4 cup milk
4 large whole eggs
2 large egg yolks
Zest of 1 lemon
1 teaspoon pure vanilla extract
1 large egg white
Heat oven to 400 degrees. Lightly brush a 20-inch nonstick deep-dish pizza pan or cake pan with butter. Dust with flour, and shake to remove any excess. Lightly brush the outside of a small ramekin with butter. Dust with flour, and shake to remove excess. Place the buttered ramekin in the center of the prepared pizza pan; set aside.
In a large mixing bowl, combine the flour, 1 1/2 cups sugar, and the baking powder. Whisk ingredients to combine.
In another large mixing bowl, whisk together the melted butter, the milk, the eggs and egg yolks, the lemon zest, and the vanilla.
Add the butter mixture to the flour mixture. Whisk together until all of the flour has been incorporated. Spoon the batter around the prepared pan, working from the inside of the pan to the outside (the pan will not be filled completely, and there will be a border from the edge of dough to pan).
In a small bowl, mix together the egg white and the remaining 1/2 cup sugar; sprinkle mixture over the batter.
Bake cake until golden brown, 20 to 25 minutes. Transfer to a wire rack. While the cake is still warm, use two forks to gently lift the ramekin out of the center of the cake. Let cake cool completely, and serve.