Position a rack in the center of the oven and heat to 325°F (165°C). Lightly butter an 8-inch square pan, line it with a parchment sling, and lightly butter the parchment.
Place the melted butter in a small bowl and stir in the lemon zest. Let it stand 2 minutes to bloom the citrus oils, then cool until just lukewarm.
In a separate small bowl, whisk together the flour and salt to evenly distribute the salt.
In a large mixing bowl, vigorously whisk the sugar and eggs for 45–60 seconds until slightly thickened and pale. Whisk in the vanilla and lemon juice until smooth.
While whisking, slowly stream in the cooled butter–zest mixture until the batter looks glossy and emulsified.
Add the flour mixture and fold gently with a spatula just until no dry spots remain. Scrape the batter into the prepared pan and smooth the top. Tap the pan once on the counter to release large air bubbles.
Bake 24–28 minutes, rotating the pan halfway through, until the surface looks matte and a toothpick near the center comes out with a few moist crumbs (not wet batter).
Cool the pan on a rack for 30–45 minutes, then lift the slab out using the parchment and set on the rack to finish cooling completely before glazing.
For the glaze, sift the powdered sugar into a bowl. Add the lemon juice and milk and whisk until smooth and thick but pourable, adjusting with a few drops of lemon juice or a spoonful of sugar as needed.
Spread the glaze over the cooled brownies. Let stand 15 minutes (or chill briefly) until set, then cut into 16 squares and serve.