Preheat oven to 350°F (175°C). Grease and flour your madeleine pan or spray it with non-stick cooking spray.
In a mixing bowl, beat the eggs and granulated sugar until light and fluffy. Then, stir in the vanilla extract.
Sift the flour, baking powder, and salt in a separate bowl.
Combine the flour mixture with the beaten eggs a little at a time and fold using a spatula until all the flour has been added. Add the grated lemon zest if using.
Slowly pour in the melted butter and continue folding until thoroughly combined. Scrape down the sides of the bowl.
Spoon the batter into the prepared madeleine molds, filling each one about three-quarters full. After filling the molds, gently tap the pan on the counter to release air bubbles for an even texture.
Bake in the preheated oven for 8-10 minutes or until the madeleines are lightly golden around the edges and spring back when lightly pressed.
Remove from the oven and let them cool in the pan for a few minutes before transferring them to a wire rack to cool completely.
Once cooled, dust the madeleines with powdered sugar if desired. Enjoy your homemade madeleines with a cup of tea or coffee!