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 1 cup 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 1 tablespoon vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Divide the batter evenly between the prepared cake 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 cakes from the oven and let them cool in the pans for 10 minutes. Then turn them out onto wire racks to cool completely.
To prepare the lemon frosting, beat 1 cup softened butter in a large bowl until creamy.
Gradually add the sifted powdered sugar, 1 cup at a time, beating on low speed until combined.
Add the lemon zest, lemon juice, 1 teaspoon vanilla extract, and heavy cream. Beat on high speed for 3-4 minutes until the frosting is light and fluffy.
If the frosting is too thick, add a little more lemon juice or cream; if too thin, add more powdered sugar.
Once the cakes are completely cooled, place one cake layer on a serving plate. Spread a layer of lemon frosting evenly over the top.
Place the second cake layer on top and frost the top and sides of the entire cake with the remaining lemon frosting.
Refrigerate the cake for 30 minutes before serving to set the frosting.