Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later. Lightly grease the parchment paper.

In a large mixing bowl, whisk together the melted butter and granulated sugar until well combined. Beat in the eggs one at a time, then stir in the vanilla extract until smooth.

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

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix, as this can lead to tough bars.

Gently fold in the lemon zest and fresh lemon juice until evenly distributed throughout the batter.

Pour the batter into the prepared baking pan and spread evenly. Bake for 25-30 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs attached (it shouldn't be completely clean, as these are meant to be fudgy).

Remove the pan from the oven and let the bars cool completely in the pan on a wire rack. This step is crucial before glazing to prevent the glaze from melting.

Once the bars are completely cool, prepare the glaze. In a medium bowl, whisk together the sifted powdered sugar and 4 tablespoons of fresh lemon juice until smooth. If the glaze is too thick, add the remaining lemon juice a teaspoon at a time until you reach a pourable but still thick consistency.

Pour the lemon glaze evenly over the cooled bars, spreading with a spatula if necessary to cover the entire surface.

Allow the glaze to set for at least 30 minutes at room temperature, or transfer the pan to the refrigerator for 15-20 minutes to speed up setting. Once the glaze is firm, use the parchment paper overhang to lift the entire slab of bars out of the pan. Place on a cutting board and slice into 16 squares (4x4 arrangement).