Preheat your oven to 350°F (175°C) and grease an 8x8-inch baking pan or line it with parchment paper for easy removal.

In a mixing bowl, combine the melted butter and granulated sugar. Stir until well combined.

Add in the eggs, one at a time, mixing well after each addition. Then, include the lemon zest, lemon juice, and vanilla extract. Mix until everything is nicely incorporated.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually fold this dry mixture into the wet ingredients until just combined. Be careful not to overmix!

Pour the brownie batter into the prepared baking pan, smoothing the top with a spatula.

Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with a few crumbs (not wet batter).

Let the brownies cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.

Optional: While the brownies are cooling, you can whip up a simple lemon glaze by mixing powdered sugar with a little lemon juice. Drizzle it over the cooled brownies for an extra zing!