Preheat the oven to 350°F. Spray an 8-inch square baking dish with nonstick cooking spray.
To a large bowl, add butter. Using a handheld mixer on medium speed, beat the butter until creamy, roughly 3-4 minutes.
Gradually add the sugar, beating until light and fluffy.
In a separate bowl, whisk together the flour, cornstarch, and baking powder.
With the mixer on low speed, alternate adding the flour mixture and milk to the butter mixture, beginning and ending with the flour mixture. After each addition, beat at a low speed just until blended.
In a separate bowl, beat the eggs with a fork. Then, gently fold the beaten eggs into the batter. Pour batter into prepared pan.
Bake for 35-38 minutes, or until a toothpick inserted in the center of the cake comes out with a few crumbs, but no wet batter.
Let the cake cool before adding the frosting.