01 - Preheat the oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
02 - In a bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
03 - In a large bowl, cream the butter and sugar with an electric mixer until light and fluffy, approximately 2 to 3 minutes.
04 - Beat in the eggs one at a time, mixing well after each addition.
05 - Add lemon zest, lemon juice, and vanilla extract. Mix until combined.
06 - Add half of the dry ingredients to the wet mixture and mix on low speed. Add the milk, then the remaining dry ingredients. Mix just until combined; do not overmix.
07 - Pour the batter into the prepared loaf pan and smooth the top evenly.
08 - Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, cover loosely with foil.
09 - Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
10 - Whisk together powdered sugar and lemon juice until smooth and pourable. Drizzle over the cooled loaf and allow icing to set before slicing.