Preheat the oven to 375°F (190°C) and grease and flour a madeleine pan.In a medium bowl, sift together the flour, baking powder, and salt. Set aside.In a large bowl, beat the eggs and granulated sugar until pale, thick, and fluffy (about 5 minutes).Gently fold in the lemon zest, lemon juice, and vanilla extract.Gradually fold the dry ingredients into the egg mixture using a spatula.Fold in the melted and cooled butter until fully incorporated.Spoon the batter into the prepared madeleine pan, filling each shell about ¾ full.Bake for 10–12 minutes, or until lightly golden and a toothpick inserted comes out clean.Cool in the pan for 2 minutes, then transfer to a wire rack.Once cooled, dust with powdered sugar if desired and serve.