Preheat your oven to 350°F (175°C). Prepare a 9x13 inch baking pan by greasing it with butter or oil, or line it with parchment paper for easy removal.
In a large mixing bowl, combine the melted butter with the granulated sugar. Use a whisk to blend them together until the mixture is smooth and well combined.
Add the eggs one at a time, whisking thoroughly after each addition. Stir in the lemon zest and fresh lemon juice until well combined.
In another bowl, sift together the all-purpose flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, stirring gently until just combined.
Pour the batter into the prepared baking pan, using a spatula to spread it evenly across the surface.
Bake the brownies in the preheated oven for 25-30 minutes. Check for doneness with a toothpick; it should come out clean or with a few moist crumbs attached. Let them cool in the pan for approximately 10 minutes, then transfer to a wire rack to cool completely.
For the glaze, mix together the powdered sugar and lemon juice until smooth. Adjust thickness with more lemon juice or powdered sugar as needed.
When the brownies have cooled completely, drizzle the lemon glaze over the top and sprinkle with extra lemon zest.
Notes
Cut the brownies into neat squares or rectangles and garnish with thin lemon slices or fresh mint.