Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened 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 vanilla extract.
Alternately add the dry ingredients and whole milk to the butter mixture, beginning and ending with the dry ingredients. Mix each addition just until combined.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 28-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes. Then, turn them out onto wire racks to cool completely.
To prepare the vanilla buttercream filling, beat the softened butter in a large bowl with an electric mixer on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Add the vanilla extract and whole milk, then beat on high speed for 3-4 minutes until the frosting is light and fluffy.
Place one cake layer on a serving plate. Spread about half of the buttercream evenly over the top.
Place the second cake layer on top and spread the remaining buttercream over the top and sides of the cake as desired.
Serve immediately or refrigerate until ready to serve. Allow the cake to come to room temperature before serving for best texture.