Preheat the oven to 350°F (175°C). Prepare an 8×8-inch baking pan by greasing it lightly or lining it with parchment paper.
In a large bowl, beat 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.
Stir in the fresh lemon juice.
Add the flour and baking powder, mixing just until combined. Do not overmix.
Pour the batter into the prepared baking pan and spread it into an even layer.
Bake for 20–25 minutes, or until a toothpick inserted into the center comes out clean.
Allow the brownies to cool for about 10–15 minutes.
In a small bowl, whisk together powdered sugar, lemon juice, and lemon zest until smooth.
Pour the glaze over the warm brownies and spread evenly. Let the Lemon Brownies cool completely before slicing.
Cut into 16 squares and serve.