Preheat oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan.

In a medium bowl, whisk together flour, baking powder, and salt.

In a large bowl, cream butter and sugar until light and fluffy, about 3-4 minutes.

Add eggs one at a time, beating well after each addition. Stir in vanilla extract and lemon zest.

Combine lemon juice and milk in a small bowl.

Add flour mixture to butter mixture in three additions, alternating with lemon juice mixture, beginning and ending with flour. Mix just until combined.

Pour batter into prepared pan and bake 50-60 minutes, until toothpick inserted in center comes out with moist crumbs.

Cool in pan for 15 minutes, then remove to wire rack.

Whisk together powdered sugar and lemon juice until smooth. Pour over warm cake.

Let cake cool completely to set glaze. Garnish with additional lemon zest before serving.