01 - Preheat oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt until evenly mixed.
03 - Using an electric mixer or whisk, beat softened butter and granulated sugar together until light and fluffy, about 2 to 3 minutes.
04 - Beat in eggs one at a time, ensuring each is fully incorporated. Mix in lemon zest, lemon juice, and vanilla extract until combined.
05 - Add half of the flour mixture to the wet ingredients, mixing on low speed. Pour in milk, then add remaining flour mixture, stirring until just combined without overmixing.
06 - Pour batter into prepared loaf pan and smooth the surface evenly.
07 - Bake for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean.
08 - Let the loaf cool in the pan for 10 minutes, then remove and transfer to a wire rack to cool completely.
09 - Whisk together powdered sugar, lemon juice, and lemon zest until smooth and drizzleable. Adjust consistency by adding more lemon juice if necessary.
10 - Drizzle the icing evenly over the cooled loaf and allow it to set before slicing.