01 - Preheat oven to 350°F. Grease a 9x5-inch loaf pan and line with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
03 - In a large bowl, combine sugar and lemon zest. Rub the zest into the sugar with your fingers until fragrant and slightly damp.
04 - Add softened butter to the lemon sugar. Beat with electric mixer until light and fluffy, about 2-3 minutes.
05 - Beat in eggs one at a time, mixing well after each addition.
06 - Mix in vanilla extract and lemon juice until combined.
07 - Add half of dry ingredients to wet mixture, mixing gently. Add milk, then remaining dry ingredients. Mix just until combined.
08 - Pour batter into prepared loaf pan and smooth top. Bake for 45-50 minutes, or until toothpick inserted into center comes out clean.
09 - Let cool in pan for 10 minutes, then transfer to wire rack to cool completely.
10 - Whisk powdered sugar with enough lemon juice to achieve thick but pourable consistency.
11 - Drizzle glaze over cooled loaf. Allow to set before slicing and serving.