Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake 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 until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the pure vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the whole milk, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter evenly into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 28 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Turn the cake out onto a wire rack and let it cool completely before serving.