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