Sift together 1 cup flour, 1 tsp baking powder, and 1/2 tsp salt in a bowl and set aside.
Butter and flour an 8x8 or 9x9 cake pan, and set aside.
With a hand or stand mixer, beat 2 eggs until creamy. Gradually add the 1 cup sugar in while still beating the eggs. Fold in the sifted ingredients. Scald the 1/2 cup milk in a small saucepan and then add 1 tbsp butter into the milk and stir until the butter is melted. Add the milk and butter into the mixing bowl all at once. Mix until incorporated. Don’t over-mix the batter. This is a thin batter.
Bake in the oven at 350 degrees for 25-30 minutes until the cake is done in the middle. It will turn golden brown on top.
When the cake is done, take it out of the oven and set it aside. Then make the frosting.