Melt the butter in a small sauce pan (or in the microwave) and set aside to cool.
Add the egg and egg yolk to a medium mixing bowl and beat together.
Add sugar, salt and vanilla to the egg and beat until light in color and creamy.
Fold the flour into the egg mixture, half at a time, until combined.
Fold in the melted butter, working quickly as not to over mix.
Refrigerate the batter while the oven is preheating. Preheat the oven to 375°F.
Melt 1 tablespoon of butter and brush it onto the madeleine mould, wipe off any excess pool of butter. Sprinkle the mould with flour, shake off the excess.
Spoon about 1 rounded tablespoon of batter in each madeleine cup, don’t flatten the batter, it will spread in the oven.
Bake for 14 minutes until you can see the side/bottom turning golden brown.
Remove from oven and transfer to a wire rack to cool.
Serve with a dusting of powder sugar.