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 all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat 1 cup softened butter and granulated sugar on medium-high speed until light and fluffy, about 4-5 minutes.
Add the eggs one at a time, beating well after each addition. Mix in 1 tablespoon vanilla extract.
With the mixer on low speed, alternately add the flour mixture and milk in three additions, beginning and ending with the flour mixture. Mix until just combined; do not overmix.
Divide the batter evenly between the prepared pans and smooth the tops with a spatula.
Bake 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, run a knife around the edges, invert onto wire racks, remove parchment paper, and cool completely.
To make the vanilla frosting, beat 1 1/2 cups softened butter on medium speed until creamy, about 2 minutes.
Gradually add the sifted powdered sugar, 1 cup at a time, beating on low speed until combined. Increase speed to medium and beat until smooth.
Add 2 teaspoons vanilla extract and 1/4 cup heavy cream. Beat on high speed for 3 minutes until light and fluffy. If frosting is too thick, add more cream 1 tablespoon at a time; if too thin, add more powdered sugar.
Place one cake layer on a serving plate and spread about 1 cup of frosting evenly 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.
Apply the remaining frosting evenly over the top and sides of the cake.
Slice and serve. Store any leftovers covered at room temperature for up to 2 days or refrigerated for up to 5 days.