Preheat the oven to 350°F. Line an 8-inch square baking dish with parchment paper and set aside. Or just spray with nonstick cooking spray (parchment helps lift them out easier later.)
To a large mixing bowl, add 1 cup (2 sticks) unsalted butter, melted and 1 ½ cups granulated sugar. Whisk until combined.
Then add in 2 large eggs, 3 Tablespoons fresh squeezed lemon juice and 1 teaspoon vanilla extract and whisk once again until well combined.
Next, add in 2 cups all purpose flour, 1 Tablespoon lemon zest and ½ teaspoon salt to the wet ingredients, and mix until just combined. Batter will be thick.
Pour the batter into the prepared baking dish and bake on the middle rack for about 20 minutes, or until the edges have cooked and the center is soft but not jiggly (it will be soft set, not hard.) Oven times can vary so please keep an eye on them and go by doneness, not time.
Allow to cool completely.
Once the lemon brownie has cooled, make the glaze by whisking together 1 cup powdered sugar and 1 ½ Tablespoons fresh squeezed lemon juice in a medium-sized bowl. Spread evenly over the cooled brownie, and allow to set before slicing and serving.
