Beat eggs and sugar until pale, thick, and ribbony (3–4 minutes).
Mix in lemon zest and vanilla.
Add sifted flour, baking powder, and salt in one go. Carefully fold until just combined.
Fold in melted butter until just incorporated.
Cover and refrigerate batter for 1 hour (or overnight for best results).
Butter and flour a madeleine pan (metal for crisper edges, silicone for easier release) and chill in the fridge while the oven preheats.
Preheat oven to 200 °C (fan 180 °C).
Spoon or pipe batter into moulds, filling each about ¾ full.
Bake 8–10 minutes until puffed and golden.
Cool 1–2 minutes, then release onto a wire rack. Dust with icing sugar before serving.