01 - Preheat oven to 350°F. Line an 8x8-inch pan with parchment paper or grease lightly.
02 - Whisk together flour, baking powder, and salt in a medium bowl. Set aside.
03 - Using a mixer, beat butter and sugar until light and fluffy.
04 - Add eggs one at a time to the butter mixture, then mix in lemon zest, lemon juice, and vanilla extract until combined.
05 - Alternate adding the flour mixture and milk to the wet ingredients, beginning and ending with flour. Stir gently until just combined; avoid overmixing.
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 - Let cake cool in pan for 10 minutes, then transfer to a wire rack to cool completely.
08 - Whisk powdered sugar and lemon juice together until smooth and drizzleable.
09 - Pour glaze over cooled cake, slice into 8 pieces, and serve.