01 - Preheat 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; set aside.
03 - Beat softened butter and sugar using an electric mixer until light and fluffy, about 3 minutes.
04 - Add eggs one at a time to the butter mixture, beating well after each addition. Stir in lemon zest and vanilla extract.
05 - Mix in fresh lemon juice; batter may appear slightly curdled, which is normal.
06 - Add half of the dry ingredients to the wet mixture and mix until just combined. Pour in milk and briefly mix. Add remaining dry ingredients and fold in gently without overmixing.
07 - Transfer batter into prepared pan and level the surface.
08 - Bake for 45 to 55 minutes until a toothpick inserted into the center comes out clean.
09 - Allow loaf to cool in pan for 10 minutes, then move to a wire rack to cool completely.
10 - Whisk powdered sugar with 2 tablespoons lemon juice, adding more juice if needed for desired consistency. Drizzle glaze over cooled loaf before slicing.