Preheat the oven to 350 degrees. Grease/spray an 8 x 8 inch baking dish (if you're looking to feed a crowd, double the recipe and use a 9 x 13 pan). Zest and juice two large lemons and set aside. In the bowl of an electric mixer, or a large bowl, beat the flour, sugar, salt, and softened butter until combined.
In a separate bowl, whisk together the eggs, lemon zest, and lemon juice until combined. Pour into the flour mixture and beat at medium speed until smooth and creamy (about 2 minutes). Pour into your greased baking dish, and bake for 23-25 minutes, or until just starting to turn golden around the edges. Insert a toothpick in the middle, and it should come out clean. Allow to cool completely.
While brownies are cooling, make your glaze. Combine the powder sugar (you can sift if you want, but I find that annoying), lemon zest and juice. Whisk it up until it looks like glaze and is not lumpy. Spread half the glaze over the brownies, let set in the fridge for about 30 minutes and then pour the remaining glaze on, and let set again.