Preheat the oven to 350°F/175°C. Line a 9x13 pan with foil and allow foil to hang over the edges to form a sling. Lightly coat the foil with nonstick cooking spray.
In a large bowl, whisk together the flour, sugar, salt, baking powder, and lemon zest.
In a separate bowl or large liquid measuring cup, whisk together the butter, eggs, egg yolks, lemon juice, and vanilla.
Add the wet ingredients to the flour mixture and stir until combined. Pour the batter into the prepared pan and spread evenly.
Bake for 25-28 minutes, until a toothpick inserted in the center comes out clean or with moist crumbs, and the top of the brownies springs back lightly when gently pressed. Don't overbake or they will be dry.
For the glaze, whisk together powdered sugar, lemon juice, and lemon zest until smooth and combined.
Let the bars cool completely in the pan, then drizzle the glaze over the top and use an offset spatula to spread evenly. Place the bars in the refrigerator for 1-2 hours to let the glaze set before lifting them from the pan, using the foil as a sling. Cut into small squares and serve. (These are best chilled, but can also be served at room temperature.)
Notes
You will probably need about 4-6 lemons for the lemon juice and zest that is in the batter and glaze. You can halve the recipe to make an 8x8 pan.