1. Preheat your oven to 350°F (175°C) and line an 8×8-inch baking dish with parchment paper, leaving some overhang for easy removal.
2. In a medium bowl, whisk together the flour, sugar, baking powder, and salt until well combined.
3. In another bowl, mix the melted butter, eggs, lemon zest, lemon juice, and vanilla extract until smooth.
4. Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix; the batter should be smooth and slightly thick.
5. Pour the batter into the prepared baking dish, spreading it evenly with a spatula.
6. Bake for 20-25 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean.
7. Allow the brownies to cool in the pan for about 10 minutes, then lift them out using the parchment paper and transfer them to a wire rack to cool completely before slicing.

These steps may remind you of the comforting, methodical process of baking with family, where each step is a chance to bond and create something delicious together.