01 - Set the oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
02 - Whisk together flour, baking powder, baking soda, and salt in a medium bowl.
03 - Using an electric mixer or whisk, beat the softened butter and sugar until light and fluffy, about 2 to 3 minutes.
04 - Add eggs one at a time, mixing thoroughly after each addition.
05 - Stir in lemon zest, lemon juice, and vanilla extract until combined.
06 - Alternately add dry ingredients and milk to the wet mixture, starting and ending with dry. Mix until just blended; avoid overmixing.
07 - Pour the batter into the prepared loaf pan and smooth the surface evenly.
08 - Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
09 - Let the cake cool in the pan for 10 minutes, then transfer to a wire rack and cool completely.
10 - Whisk powdered sugar with enough lemon juice to form a thick yet pourable glaze.
11 - Drizzle the lemon icing over the cooled loaf and allow to set before slicing.