Preheat oven to 350°F. Grease three 8 or 9" cake pans, line with parchment paper, and grease the parchment paper, too.
In a medium bowl, whisk the sifted flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and sugar until smooth and creamy. Add eggs, 1 at a time, and mix until just combined after each. Add vanilla extract and sour cream and mix until smooth, scraping down the sides of the bowl as needed.
Add dry ingredients to wet ingredients in 3 additions and mix until just combined after each. Add the milk and mix until smooth. Do not overmix.
Divide the batter evenly into the prepared cake pans. Bake for 22-24 minutes until a toothpick inserted into the center comes out clean. If your cakes are baking unevenly, rearrange them in the oven midway through baking.
Allow the cakes to cool slightly in the pan and then cool completely in the fridge before topping.