Heat the oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper, leaving enough overhang on two sides to lift out the cooled brownies. A 9-inch square pan may be used for thinner brownies.

Rub the lemon zest into the granulated sugar with your fingertips, then whisk the lemon sugar with the melted, slightly cooled butter until smooth. Beat in the room-temperature eggs, fresh lemon juice, and remaining lemon zest.

Add the all-purpose flour and salt to the wet mixture. Stir just until no dry streaks remain, taking care not to overmix the batter.

Spread the batter evenly in the prepared pan. Smooth the surface so the brownies bake to an even thickness.

Bake at 350°F (175°C) for 25-30 minutes, until the edges are lightly golden and the center is set. A toothpick inserted in the center should come out with a few moist crumbs rather than wet batter.

Cool the brownies completely in the pan before glazing. Whisk the powdered sugar, lemon zest, and 2 tablespoons of lemon juice, adding the remaining lemon juice gradually until the glaze is thick but spreadable.

Spread the glaze over the cooled brownies and let it set. For sharp cuts, refrigerate the glazed brownies briefly, lift them out using the parchment, and slice with a knife wiped clean between cuts.