Preheat oven to 350°F (175°C) and grease an 8-inch round cake pan.
Whisk together flour, baking powder, and salt in a bowl.
In a separate bowl, cream butter and sugar until light and fluffy. Add eggs one at a time, then vanilla extract.
Gradually add dry ingredients to wet ingredients, alternating with milk. Mix until smooth.
Pour batter into the prepared pan and bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
Cool completely before assembling.