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 flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix each addition just until combined.
Divide the batter evenly between the prepared cake pans and smooth the tops.
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.
Run a knife around the edges and invert the cakes onto wire racks to cool completely.
While the cakes cool, prepare the lemon frosting: In a large bowl, beat the softened butter until creamy.
Gradually add the powdered sugar, one cup at a time, beating on low speed until combined.
Add the fresh lemon juice, lemon zest, 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 more heavy cream, one teaspoon at a time, until desired consistency is reached.
Place one cake layer on a serving plate and spread a layer of lemon frosting evenly on 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.