Preheat your oven to 375°F (190°C). Prepare a madeleine pan by greasing it lightly with butter or cooking spray.

In a mixing bowl, whisk together the eggs and granulated sugar until the mixture becomes pale and slightly thickened, about 3-5 minutes.

Stir in the vanilla extract and lemon zest (if using) into the egg mixture.

In a separate bowl, combine the sifted flour, baking powder, and salt. Gradually fold the dry ingredients into the egg mixture using a spatula, being careful not to deflate the batter.

Pour in the melted butter and gently fold it into the batter until fully incorporated. The batter should be smooth and thick.

Spoon the batter into the prepared madeleine pan, filling each mold about 3/4 full.

Bake in the preheated oven for 10-12 minutes or until the edges are golden brown and a toothpick inserted into the center comes out clean.

Remove the madeleines from the oven and let them cool in the pan for about 5 minutes. Then, gently remove them from the pan and transfer them to a wire rack to cool completely.

Dust with powdered sugar before serving, if desired.