Preheat your oven to 350°F (175°C) and prepare an 8x8" pan by spraying it with cooking spray or lining it with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and lemon zest until light and fluffy. Add the eggs one at a time, mixing well after each addition, then add the fresh lemon juice. Gently fold in the flour and baking powder until just combined.
Pour the batter into the prepared pan and smooth it into an even layer. Bake for about 20–25 minutes or until a toothpick inserted into the center comes out clean. Allow to cool in the pan for about 10–15 minutes.
Prepare the glaze by whisking together the powdered sugar, fresh lemon juice, and lemon zest until smooth. Pour it over the cooled brownies and spread evenly.
Let the glazed brownies cool completely before slicing them into squares.