1Melt the unsalted butter in a small saucepan over low heat, then set aside to cool.
In a mixing bowl, whisk together the all-purpose flour, baking powder, and salt.
In another bowl, beat the eggs and granulated sugar together until the mixture is pale and thick.
Stir in the vanilla extract and lemon zest into the egg mixture.
Gently fold the dry ingredients into the wet ingredients until just combined.
Gradually add the melted butter, folding it in until the batter is smooth.
Cover the batter and refrigerate for at least 1 hour or overnight.
Preheat the oven to 375°F (190°C) and butter a madeleine pan.
Spoon the batter into the madeleine molds, filling each about three-quarters full.
Bake for 10-12 minutes, or until the edges are golden brown and the centers spring back when lightly touched.
Remove from the oven and let cool in the pan for a few minutes before transferring to a wire rack to cool completely.
Serve the madeleines warm or at room temperature, optionally dusted with powdered sugar.