Preheat your oven to 350°F (175°C). Lightly grease an 8×8-inch baking pan or line it with parchment paper.
Whisk together the gluten-free flour, baking powder, and salt in a medium bowl. Set aside.
In a large bowl, combine the granulated sugar and melted butter, stirring until smooth. Add the eggs, one at a time, mixing well after each addition. Stir in the lemon juice, lemon zest, and vanilla extract until fully incorporated.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix.
Pour the batter into the prepared baking pan, spreading it evenly. Bake for 20-25 minutes or until a toothpick inserted into the centre comes out clean. Allow the brownies to cool completely in the pan.
In a small bowl, whisk together the powdered sugar, lemon juice, and lemon zest until smooth.
Once the brownies have cooled, pour the glaze over the top, spreading it evenly with a spatula. Allow the glaze to set before cutting the brownies into squares.