01 - Preheat the oven to 350°F. Grease and flour a 9x5-inch loaf pan.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
03 - In a large bowl, beat the butter with sugar until light and fluffy, about 3 minutes.
04 - Beat in eggs one at a time, blending thoroughly after each addition. Stir in lemon zest, lemon juice, and vanilla extract.
05 - Add flour mixture in three parts alternated with milk, starting and ending with flour. Mix until just combined; avoid overmixing.
06 - Pour batter into prepared pan and smooth surface evenly.
07 - Bake for 40 to 45 minutes, or until a toothpick inserted in the center comes out clean.
08 - Allow cake to cool in pan for 10 minutes, then transfer to wire rack to cool completely.
09 - Whisk powdered sugar with lemon juice until smooth. Drizzle over cooled cake and allow to set before slicing.