Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, sift together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3 to 5 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the pure vanilla extract.
Alternately add the dry ingredients and whole milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Pour the batter evenly into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 28 to 32 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 for 10 minutes.
Turn the cake out onto a wire rack and cool completely before serving.