Preheat the oven to 350°F (175°C). Grease and flour two 8-inch round cake pans or line them with parchment paper.
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 3-5 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract and finely grated lemon zest until evenly combined.
With the mixer on low speed, alternately add the dry ingredients and the milk to the butter mixture, beginning and ending with the dry ingredients. Mix 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 28-32 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.
Run a knife around the edges to loosen the cakes, then turn them out onto wire racks to cool completely before frosting or serving.