01 - Preheat oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
03 - In a large bowl, beat butter and sugar until light and fluffy, about 2 to 3 minutes.
04 - Add eggs one at a time, beating well after each addition.
05 - Mix in lemon zest, lemon juice, and vanilla extract until evenly combined.
06 - Add half the flour mixture and mix gently. Stir in the milk, then the remaining flour mixture. Mix until just combined; avoid overmixing.
07 - Pour batter into the prepared loaf pan and smooth the surface.
08 - Bake for 45 to 50 minutes or until a toothpick inserted in the center comes out clean.
09 - Cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
10 - Whisk powdered sugar and lemon juice together until smooth and pourable, adjusting consistency with additional lemon juice if necessary.
11 - Drizzle the icing over the cooled loaf. Allow the icing to set before slicing.