Preheat the oven to 350°F. Prepare an 8-inch square pan with butter and flour or baking spray.
Beat the butter at medium speed with a handheld mixer until creamy, roughly 3-4 minutes.
Gradually add the sugar, beating until light and fluffy.
Sift together the flour, corn starch, and baking powder.
Add the flour mixture to the butter mixture alternately with the milk, beginning and ending with the flour mixture. Beat at a low speed just until blended after each addition.
In a separate bowl, beat the eggs with a fork and then gently fold the beaten eggs into batter. Pour batter into prepared pan.
Bake for 35-38 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Let the cake cool before adding the frosting.