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 softened butter and granulated sugar until light and fluffy, about 2 to 3 minutes.
04 - Add eggs one at a time, beating well after each addition.
05 - Stir in finely grated lemon zest, fresh lemon juice, and vanilla extract.
06 - Add half the flour mixture and mix gently, then add milk and mix. Finally, add remaining flour mixture and stir until just combined, taking care not to overmix.
07 - Pour batter into the prepared loaf pan and smooth the surface evenly.
08 - Bake for 45 to 50 minutes, or until a toothpick inserted in the center comes out clean.
09 - Allow cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
10 - Whisk powdered sugar and lemon juice together until smooth and pourable. Adjust consistency by adding lemon juice if necessary.
11 - Once cooled, drizzle lemon icing over the top and allow it to set before slicing.