Preheat oven to 350F. Line a 8x8-inch square metal baking dish with parchment paper. Set aside.
Add the granulated sugar and lemon zest to a large bowl. Rub the zest into the sugar with your fingers until the lemon oils have released from the zest and the sugar is light yellow and fragrant. You can also do this in your food processor.
Add the melted butter to the sugar mixture. Mix for 1-2 minutes, until smooth.
Add the eggs, lemon juice, lemon extract, and salt to the butter mixture. Mix until combined.
Gradually add the gluten-free flour to the wet ingredients. Stir until no more steaks of flour remain.
Pour the batter into the prepared baking dish. Bake at 350F for 22-25 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs. Do not overbake.
Let the lemon brownies cool completely before adding the glaze.
To make the glaze, combine the powdered sugar, lemon juice and lemon zest in a bowl and whisk until smooth.
Pour the glaze over the top of the lemon brownies. Let set before slicing and serving. You can place it in the refrigerator for 30 minutes to speed up the process.