01 - Preheat the 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. Using your fingers, rub the zest into the sugar until fragrant and slightly damp.
04 - Add softened butter to the lemon sugar and beat with an electric mixer until light and fluffy, about 2-3 minutes.
05 - Beat in the eggs, one at a time, mixing well after each addition.
06 - Mix in the vanilla extract and lemon juice.
07 - Add half of the dry ingredients to the wet mixture, mixing gently. Add the milk, then the remaining dry ingredients. Mix just until combined; do not overmix.
08 - Pour the batter into the prepared loaf pan and smooth the top.
09 - Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
10 - Remove from oven and let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
11 - To make the glaze, whisk powdered sugar with enough lemon juice to achieve a thick but pourable consistency.
12 - Drizzle the glaze over the cooled loaf. Allow to set before slicing and serving.