Preheat oven to 350°F (175°C).
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the butter and sugar together until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract.
Alternate adding the flour mixture and milk to the butter mixture, mixing just until incorporated.
Grease a 9-inch pie dish and pour the batter into it.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow to cool completely before serving.
