Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
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 1/2 cup softened butter and granulated sugar until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in 2 teaspoons 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.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 28 to 30 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes. Then transfer to a wire rack to cool completely.
To prepare the lemon frosting, beat 1/2 cup softened butter in a large bowl until creamy.
Gradually add powdered sugar, 1 cup at a time, beating on low speed until combined.
Add fresh lemon juice, lemon zest, heavy cream, and vanilla extract. Beat on high speed for 2 to 3 minutes until the frosting is light and fluffy.
Once the cake is completely cooled, spread the lemon frosting evenly over the top and sides of the cake.
Slice and serve.