Preheat the oven to 350°F (180°C).

Butter or spray an 8-inch square baking pan. You can line it with a strip of parchment paper, covering the pan's bottom and two long sides. The two short sides will remain unlined but greased. I recommend it as it will help you to easily remove the bars from the pan.

Mix ½ cup unsalted butter with 1 cup white sugar with a whisk until smooth.

Add 2 eggs and integrate. Mix well, but don't beat too much.

Fold in 1 tablespoon lemon zest and ½ teaspoon vanilla extract.

Add the sifted 1 cup all-purpose flour and ½ teaspoon salt. You can sift them before or have the ingredients measured and sift them directly over the butter mixture (my choice).

Mix until it's all well incorporated, but don't overbeat.

Add 3 tablespoons fresh lemon juice and mix just until combined.

Fill the prepared pan with this batter and even out the top.

Bake for about 20 minutes, until almost set in the center. This is key to prevent them from drying out. A toothpick or cake tester inserted in the center should come out with moist crumbs but not wet.

Let cool on a wire rack for 10-15 minutes, and then cover loosely with a clean kitchen towel. Cool almost completely before glazing.

When ready to eat, run a smooth-bladed knife around the edges of the pan to loosen any stuck bits, and then use the paper to lift the whole block of lemon brownies. Transfer to a flat surface and cut.

Mix 1 cup powdered sugar with 2 tablespoons fresh lemon juice in a medium bowl until creamy and thick.

Pour and spread the glaze on the lemon brownies with an offset spatula or the back of a spoon. Sprinkle with fresh lemon zest if you want to. Let the glaze dry before cutting, or cover the pan with plastic wrap and chill until ready to eat.

It can be made ahead and stored in an airtight container in the refrigerator for 2 weeks. Mix well before using.