Preheat the oven to 350°F (175°C). Grease and flour two 8-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 unsalted butter and granulated sugar together using 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 lemon zest and lemon juice until combined.
Add the vanilla extract.
Alternately add the dry ingredients and the whole milk to the butter mixture, beginning and ending with the dry ingredients. Mix each addition just until combined; do not overmix.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Remove the cakes from the oven and let them cool in the pans for 10 minutes.
Turn the cakes out onto wire racks and let them cool completely before frosting or serving.
Optional: Dust the cooled cakes with powdered sugar before serving for a simple finish.