Preheat oven to 350°F Grease bottom and sides of one 9" round cake pan. Line bottom with parchment paper and set aside.
In a bowl, whisk together eggs, half the milk, and the vanilla.
In another bowl, whisk together flour, sugar, baking powder, lemon rind and salt. Using an electric mixer, beat dry ingredients with remaining milk and butter at medium speed for 2 minutes until fluffy. Add egg mixture 1/3 at a time, mixing well and scraping down sides of bowl between additions.
Transfer batter to prepared pan. Bake in preheated oven 30 minutes or until cake tester comes out clean from center. Cool in pan 10 minutes. Run a thin-bladed knife around the edge of the pan, then turn cake out onto a rack until fully cooled. Peel off parchment paper before slicing.