Preheat oven: to 180°C (350°F). Grease and flour a 9x13 inch baking dish.

Combine dry ingredients: Whisk together flour, cornstarch, and baking powder in a medium bowl.

Cream butter and sugar: In a large bowl, cream together softened butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in lemon zest.

Combine wet and dry ingredients: Gradually add dry ingredients to wet ingredients, mixing until just combined.

Prepare the baking dish: Pour batter evenly into prepared baking dish.

Whisk ingredients: In a medium bowl, whisk together egg, sugar, vanilla extract, and cornstarch until smooth.

Combine with milk: Gradually whisk in milk until mixture is smooth.

Cook the pudding: Pour pudding mixture over cake batter in the baking dish.

Bake: Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Let cool slightly before serving.

For an extra special touch, serve with whipped cream or a scoop of vanilla ice cream.