Preheat the oven to 350°F (180°C). Grease and flour a 9-inch cake pan.
In a mixing bowl, cream the butter and sugar together with an electric mixer until light and fluffy.
In another bowl, sift together the flour, baking powder, and salt.
Add the eggs to the butter mixture, one at a time, beating well after each addition.
Add the flour mixture to the butter mixture in three parts, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Stir in the vanilla extract.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Remove the cake from the pan and transfer it to a wire rack to cool completely.