Madeleines

Preheat the oven to 180 °C (360 °F).
Soften 180 g of butter by putting it in the microwave for 10 seconds.

In a cul-de-poule, whisk the 4 whole eggs with 160 g of sugar until you obtain a "ribbon" (it should "whiten". This can take several minutes).
Add 180 g of flour and 8 g of baking powder altogether.
Mix well.
Add the softened butter.
Work the dough well so that it becomes homogeneous.
At the last moment, add 2 cl of rum.

Using a pastry bag, place the dough in the madeleine molds without filling them too much. (If they are not made with silicone, butter them and flour them first).

Bake (10 min for small sizes, and 15 min for larger ones).

Serve warm preferably.

Notes:
In commerce, the "duchess" is a butter madeleine (without palm oil ...) and the "royal" must contain at least 22% butter.

Regarding the invention, it would have been immortalized by the cook Madeleine Paumier, in Commercy (hence the name of the pastry); but remember that many stories exist.

Select madeleine molds of small size. A metal mold transfers better the heat and will create a nice small crust. 2 shapes exist: scallop shell, or long sticks.
You can add super tiny zest of organic lemons ("non traités"/not-treated, only means AFTER harvest). Orange blossom can replace rum. Icing (40 g icing sugar + 10 cl orange juice) can be brushed just out of the oven, then put back 30 sec in very hot oven.
Prepare molds full or dough ahead. Bake at the last minute to serve warm at the end of the meal (w/ coffee). This will call for superb digestif. Madeleines were invented in Commercy, France, but how remains very debated.