Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the pure vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix on low speed just until combined after each addition.
Pour the batter evenly into the prepared baking pan and smooth the top with a spatula.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan on a wire rack for 15 minutes.
Run a knife around the edges to loosen the cake, then invert onto a serving plate or cool completely in the pan before slicing and serving.