Line an 8X8 inch baking dish with aluminum foil, overhanging the edges 2 inches on two opposing sides. Spray with nonstick cooking spray and set aside. Preheat oven to 350 degrees.
In the bowl of a stand-up mixer, add the flour, sugar, salt, and butter and beat until well combined.
In a separate bowl, add the eggs, lemon zest, and lemon juice and mix until well combined. Add this egg mixture to the flour mixture and beat on medium speed for 2 minutes until mixture is smooth and creamy.
Pour batter into prepared baking dish and using an offset spatula, smooth out the top of the batter. Bake in preheated oven for 20-25 minutes, or until the edges just begin to turn golden or a toothpick inserted in the center of the brownies comes out clean or with a few moist crumbs. Cool the brownies completely in the pan set on a wire baking rack before applying the glaze.
Make the glaze by sifting the powdered sugar into a large mixing bowl. Add 1 1/2 tablespoons of lemon juice to powdered sugar and using a hand-held electric mixer, beat until the juice is completely combined. Add more lemon juice, 1 teaspoon at a time, until glaze reaches a thick but just spreadable consistency. Pour glaze onto the center of the completely cooled Lemon Brownies and use an offset spatula to spread and cover the surface. Sprinkle the top with remaining 2-3 teaspoons of lemon zest. I recommend refrigerating overnight, then removing from the pan, and cutting into bars.