01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper or grease lightly.
02 - Whisk together all-purpose flour, baking powder, and salt in a medium bowl. Set aside.
03 - Using a mixer, beat softened butter and granulated sugar until light and fluffy.
04 - Beat in eggs one at a time, then add lemon zest, lemon juice, and vanilla extract, mixing until homogenous.
05 - Alternately add flour mixture and milk to the wet ingredients, starting and ending with flour. Mix until just combined.
06 - Pour batter into prepared pan and smooth surface. Bake for 28 to 32 minutes or until a toothpick inserted in the center comes out clean.
07 - Allow cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
08 - Whisk powdered sugar with lemon juice until smooth and pourable.
09 - Drizzle glaze over cooled cake. Slice into 8 portions and serve.