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, baking soda, 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 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the sour cream, fresh lemon juice, lemon zest, and vanilla extract until combined.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 28-30 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer the cake to a wire rack to cool completely.
While the cake cools, prepare the lemon frosting: In a large bowl, beat 1/2 cup softened butter until creamy.
Gradually add the powdered sugar, beating on low speed until combined.
Add the fresh lemon juice and lemon zest and beat on medium speed until smooth.
If the frosting is too thick, add heavy cream 1 tablespoon at a time until desired consistency is reached.
Once the cake is completely cool, spread the lemon frosting evenly over the top and sides of the cake.
Slice and serve.