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.

Whisk the melted and slightly cooled butter with the granulated sugar until smooth. Add the eggs, lemon zest, and lemon juice, then whisk until the mixture is evenly combined.

In a separate bowl, combine the all-purpose flour, baking powder, and fine salt. Fold the dry ingredients into the lemon mixture just until no dry streaks remain.

Spread the batter evenly in the prepared pan. Bake at 350°F (175°C) for 22 to 28 minutes, until the edges are lightly golden and the center is set but still slightly soft.

Cool the brownies completely in the pan. Stir the powdered sugar and lemon juice into a thick glaze, add the optional zest, spread it over the brownies, let it set, and slice into 16 squares.