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 using 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 1 tablespoon of vanilla extract.
With the mixer on low speed, alternately add the flour mixture and the whole milk to the butter mixture, beginning and ending with the flour mixture. 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 28-30 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, turn them out onto wire racks to cool completely.
For the cream cheese frosting, beat the softened cream cheese and 1/2 cup softened butter together on medium speed until smooth and creamy, about 2-3 minutes.
Gradually add the sifted powdered sugar, one cup at a time, beating on low speed until incorporated. Increase speed to medium and beat until fluffy.
Mix in 1 teaspoon of vanilla extract until combined.
Once the cakes are completely cool, place one cake layer on a serving plate. Spread a thick, even layer of cream cheese frosting over the top.
Place the second cake layer on top and frost the top and sides of the entire cake with the remaining cream cheese frosting.
Refrigerate the cake for at least 30 minutes before serving to set the frosting.