Add butter to a small saucepan. Melt the butter over medium heat. Cook until the butter has melted. Remove from the heat and pour into a heat-proof bowl and leave to cool to room temperature.
In the bowl of the stand mixer place the eggs and sugar and whip on high speed until the mixture is thick and pale, for about five minutes.
Mix in vanilla extract.
In a large mixing bowl sift together flour, baking powder and salt. Add the flour to the egg mixture and using a spatula, gently fold into the egg mixture.
Add the melted butter and using a spatula, fold the butter into the mixture. Take care not to over mix.
Cover the batter with cling film and refrigerate for at least 1 hour or overnight.
At least 15 minutes before your are ready to bake, pre-heat the oven to 160°C. Using a pastry brush, lightly brush the pan with melted butter, then lightly dust with flour. Shake off any excess flour from the pan.
Using a tablespoon, fill the deepest part of the mould with 1 level tablespoon of the batter. You do not need to spread the batter. Cover and refrigerate any remaining batter.
Bake for 10-12 minutes. The madeleines are ready when the humps have risen and bounce back when lightly pressed. Remove from the oven and allow to cool on a wire rack for 10 minutes. Invert and lightly tap the pan to release the madeleines from the pan and place on a wire rack to cool completely.
Melt chocolate in 30 second bursts in the microwave until melted. Dip each madeleine in melted chocolate and decorate with sprinkles.