In France, the little cakes called Madeleines are well loved and often enjoyed. The cities of Commercy, Reims, and Epernay are particularly noted for their Madeleines. Based on extensive work with formulating Madeleines, both for retail and wholesale production, I hope the following notes will be useful.
Madeleines are made from flour, butter, eggs, both whites and yolks, and sugar, normally in equal proportions. Baking powder or ammonium carbonate is often added to the batter as a leavening agent to help achieve a light Madeleine. Because of their light, aerated texture Madeleines conserve badly.

There are many methods to prepare a traditional, classic Madeleine batter, each producing its own texture, flavor profile, and set of keeping qualities.

The eggs can be stiffly beaten while warm, they will rise fast and high. They can be beaten while cold: the volume achieved is less, but the batter is more mousse like and conserves longer. In this case the eggs are first beaten with the sugar, then, when they are well beaten, the flour and melted butter are added.

The softened butter and sugar can also be beaten together, incorporating the eggs one by one. When the batter is well beaten and fluffy, the flour is folded in. The batter obtained by this method is thick, and baking powder made be added: this batter rises well and 20-32 eggs per kilo of flour can be incorporated, providing the longest conservation. Finally, the batter can be made the same way as above, while mixing only egg yolks into the sugar-butter mixture and beating the whites stiffly.

The batter is dispensed into buttered, floured Madeleine molds, and filled about 2/3 full. It is either allowed to sit to thicken, or baked immediately, depending on the leavener used. It is baked at about 375°C/190°F for about 10 minutes. The cakes are removed from their pans shortly after baking.

Note that premium quality Madeleines are made with many eggs and a high proportion of butter. Lesser quality Madeleines have fewer eggs and some of the butter replaced by milk. Most of the butter available in the United States, is more lightly flavored than European butter, so a premium Madeleine made in North America will not use the maximum quantity of eggs as their flavor will dominate over the butter.

It is the egg/butter balance (especially using American butter) that determines the flavor profile.

Note that a classic French Madeleine may also be made with a lightly browned butter. This lends a unique, and particularly lovely flavor that is unusual to find in the United States, and it well compliments our characteristically more bland flavored butter. It is a lovely accent to either lemon or vanilla Madeleines. The butter must be browned just a bit to enrich its flavor very subtly and not lend a strong caramelized taste to the traditional buttery Madeleine flavor.