01 - Preheat oven to 350°F. Grease and flour a 9x5-inch loaf pan or line it with parchment paper.
02 - Whisk flour, baking powder, and salt in a medium bowl until evenly mixed.
03 - In a large bowl, beat softened butter with granulated sugar using an electric mixer until light and fluffy, about 3 minutes.
04 - Add eggs one at a time, mixing well after each addition. Stir in lemon zest and vanilla extract until combined.
05 - Pour in freshly squeezed lemon juice and mix briefly; a slightly curdled mixture is expected.
06 - Alternately add the flour mixture and milk to the wet ingredients, beginning and ending with flour. Mix gently until just combined to avoid overmixing.
07 - Pour batter into prepared pan and smooth the surface evenly.
08 - Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
09 - Allow cake to cool in the pan for 10 minutes before transferring to a wire rack.
10 - Whisk powdered sugar with enough lemon juice to form a smooth glaze. Drizzle over cooled loaf and allow to set before slicing.