Start by preheating your oven to 350°F and preparing an 8×8-inch baking pan with parchment paper or nonstick cooking spray. In your stand mixer with the paddle attachment, beat together the softened butter, sugar, and lemon zest until the mixture becomes light and creamy. This process incorporates air into the batter for a better texture.

Add the eggs, vanilla extract, and two tablespoons of lemon juice to the butter mixture and beat until everything is well combined. The batter should look smooth and unified. Mix in the flour, salt, and baking powder, stirring just until the dry ingredients are incorporated. Be careful not to overmix, as this can make your brownies tough instead of tender.

Pour the batter into your prepared pan and spread it evenly. Bake for 25-30 minutes, checking at the 25-minute mark with a toothpick. When it comes out clean, your brownies are done.

Let the brownies cool in the pan for 10-15 minutes. While they're cooling, whisk together the powdered sugar, remaining lemon juice, and zest of half a lemon to create your glaze.

Pour the glaze over the slightly cooled brownies and spread it evenly across the top. Allow the glaze to set for another 10-15 minutes before slicing and serving.