Preheat your oven to 325°F (165°C).
Line a 9×13-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal.
Lightly grease the parchment paper with cooking spray or butter.
In a large bowl, whisk together the melted butter, granulated sugar, and lemon zest until well combined.
Add the eggs one at a time, whisking well after each addition until fully incorporated.
Stir in the lemon juice and vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined.
Pour the batter into the prepared pan, spreading it evenly to the edges.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow the brownies to cool completely in the pan on a wire rack before glazing.
In a medium bowl, whisk together the powdered sugar, lemon juice (starting with 3 tablespoons), and lemon zest until smooth.
Pour the glaze over the cooled brownies, spreading it evenly with a spatula.
Allow the glaze to set for about 30 minutes before cutting into squares.