Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans and line the bottoms with parchment paper.
In a medium bowl, whisk together the sifted flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the softened butter with an electric mixer on medium speed until creamy, about 1 minute.
Gradually add the granulated sugar and continue beating until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
With the mixer on low speed, alternately add the dry ingredients and the milk in three additions, beginning and ending with the dry ingredients. Mix just until combined; do not overmix.
Divide the batter evenly between the prepared cake pans and smooth the tops 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 cakes from the oven and let them cool in the pans for 10 minutes. Then invert the cakes onto a wire rack, remove the parchment paper, and let them cool completely.
To make the vanilla buttercream frosting, beat the softened butter in a large bowl on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar, 1 cup at a time, beating on low speed until combined.
Add the vanilla extract, milk, and a pinch of salt. Beat on high speed for about 3 minutes until the frosting is light and fluffy. Adjust the consistency by adding more milk if too thick or more powdered sugar if too thin.
Place one cake layer on a serving plate or cake stand. Spread a thick, even layer of frosting over the top.
Place the second cake layer on top and apply a thin crumb coat of frosting over the entire cake. Chill for 15 minutes in the refrigerator.
Remove the cake from the refrigerator and apply the final layer of frosting smoothly over the cake.
Decorate as desired with sprinkles, piped frosting, or other birthday decorations.
Serve at room temperature. Store any leftovers covered in the refrigerator for up to 4 days.