Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, beat the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Begin and end with the flour mixture. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top. Bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.