Melt butter and let it cool slightly. Whisk eggs and sugar with an electric mixer for 8 minutes until thick, pale, and ribbon-like, then add the vanilla.
Sift flour, baking powder, and salt, then fold half into the egg mixture. Stir ¼ cup of batter into the melted butter until fully incorporated, then mix it back into the main batter. Chill the batter and the tray for 30-60 minutes to ensure the signature bump.
Preheat the oven to 220°C (200°C fan-forced). Brush the cold madeleine tray with melted butter and spoon batter into each scalloped well. A scalloped tray is ideal for the traditional shape, but a muffin tray can be used as an alternative.
Reduce the oven temperature to 200°C (180°C fan-forced) and bake for 10-12 minutes until golden brown. Transfer warm madeleines to a wire rack to cool.
