Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the butter and sugar on medium-high speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Reduce the mixer speed to low and add the flour mixture in three additions, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared pan and spread it evenly.
Bake for 30-35 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Allow the cake to cool completely in the pan on a wire rack.