01 - Preheat oven to 350°F. Grease and line an 8x8-inch square baking pan with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, and salt.
03 - In a large bowl, beat butter and sugar together until light and fluffy, approximately 2-3 minutes.
04 - Add eggs one at a time, beating well after each addition. Stir in lemon zest, lemon juice, and vanilla extract.
05 - Gradually add the flour mixture, alternating with milk, mixing until just combined.
06 - Pour the batter into the prepared pan and smooth the top with a spatula.
07 - Bake for 28-32 minutes, or until a toothpick inserted in the center comes out clean.
08 - Allow the cake to cool completely in the pan on a wire rack, approximately 1 hour.
09 - Beat cream cheese and butter together until smooth and creamy.
10 - Add powdered sugar, lemon juice, lemon zest, vanilla extract, and salt. Beat until light and fluffy.
11 - Once the cake is cool, spread the frosting evenly over the top using an offset spatula or butter knife.
12 - Cut into 8 equal slices and serve immediately.