Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, then line the bottoms with parchment paper circles.
In a medium bowl, whisk together the sifted 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.
With the mixer on low speed, alternately add the dry ingredients and the milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just 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 28-32 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 run a knife around the edges, invert the cakes onto wire racks, remove the parchment paper, and 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 sifted powdered sugar, about 1 cup at a time, beating on low speed until combined. Add the vanilla extract and 2 tablespoons of whole milk, then beat on high speed for 3 minutes until light and fluffy. Add more milk if needed to reach a spreadable consistency.
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 as desired.
Serve immediately or refrigerate until ready to serve. Bring to room temperature before serving for best texture.