Preheat your oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan, or line with parchment paper, leaving an overhang on the long sides for easy lifting. This helps prevent sticking and makes removal simple.

In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.

In a large mixing bowl, combine the granulated sugar and lemon zest. Rub the zest into the sugar with your fingertips for a minute or two until the sugar is fragrant and appears slightly yellow. This technique helps to infuse the sugar with more intense lemon flavor.

Add the slightly cooled melted butter to the lemon sugar mixture and whisk until well combined and smooth.

Whisk in the eggs one at a time, ensuring each egg is fully incorporated into the batter before adding the next. This creates a more emulsified and stable batter.

Stir in the whole milk, 2 tablespoons of fresh lemon juice, and vanilla extract until the wet ingredients are thoroughly combined.

Gradually add the dry ingredients from the medium bowl to the wet ingredients in the large bowl. Mix on low speed with an electric mixer or by hand with a whisk until just combined. Be careful not to overmix; overmixing can lead to a tough loaf. A few small lumps are perfectly fine.

Pour the batter evenly into the prepared loaf pan.

Bake for 50-60 minutes, or until a wooden skewer or toothpick inserted into the center of the loaf comes out clean. If the top starts to brown too quickly during baking, you can loosely tent it with aluminum foil to prevent excessive browning.

Remove the loaf from the oven and let it cool in the pan on a wire rack for 10-15 minutes. This allows the loaf to set before handling.

While the loaf cools, prepare the lemon glaze. In a small bowl, whisk together the sifted powdered sugar and 3 tablespoons of fresh lemon juice until smooth and lump-free. For a thicker glaze, add more powdered sugar; for a thinner glaze, add more lemon juice ½ teaspoon at a time until you reach your desired pourable but not watery consistency.

After the loaf has cooled slightly in the pan, use the parchment paper overhang (if used) or carefully invert the pan to lift it out and place it directly onto the wire rack. Place a piece of parchment paper or foil underneath the rack to catch any glaze drips for easy cleanup.

While the loaf is still warm (but not hot to the touch), pour the lemon glaze evenly over the top, allowing it to slowly drip down the sides for a rustic look.

Let the glaze set for at least 30 minutes at room temperature before slicing and serving. This ensures the glaze hardens slightly.