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.
03 - In a large bowl, cream the butter and sugar together until light and fluffy, about 2–3 minutes.
04 - Beat in the eggs, one at a time, mixing well after each addition. Add lemon zest, lemon juice, and vanilla extract; mix to combine.
05 - Add half of the flour mixture to the wet ingredients and mix on low speed. Add the milk, then the remaining flour mixture, mixing until just combined. Do not overmix.
06 - Pour the batter into the prepared loaf pan and smooth the top.
07 - Bake for 50–55 minutes, or until a toothpick inserted into the center comes out clean.
08 - Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
09 - For the icing, whisk together powdered sugar, lemon juice, and lemon zest until smooth and pourable. Adjust consistency with more lemon juice if needed.
10 - Drizzle the icing over the cooled loaf. Let set before slicing.