Weigh your butter, melt it and set it aside to cool.
Combine eggs and sugar in the bowl of a stand mixer with a paddle or whisk attachment. I used both and give a slight edge to the whisk. Set your mixer on HIGH and blend for 8 minutes, until the mixture is pale in color and holds a ribbon when a spatula spoons up some of the batter
While the eggs and sugar are whipping up, combine the sifted flour with the salt, baking powder, cinnamon, ginger, and cardamom.
Remove the bowl from the mixer.
GENTLY fold in the flour/spice mixture, one-third of the flour mixture at a time, by scraping along the bottom of the bowl with a spatula (wide is good) towards you. Continue up the side and scoop the mixture over the top. Rotate the bowl a quarter of a turn and repeat the process. Continue rotating and folding until the flour is just combined...don't overfold.
Add the vanilla to the milk and GENTLY fold the vanilla/milk combination into the flour mixture.
Then, GENTLY fold in the cooled butter using the same technique.
The key is GENTLE AND SLOW. You built up a lovely air-filled batter when you beat the eggs and sugar; you don't want to deflate it now.
Transfer the batter to a smaller bowl with a lid or cover the large mixing bowl and refrigerate for at least 60 minutes.
At the same time, put your madeleine pans in the freezer. After 10 minutes, remove your madeleine pans and brush them with melted butter. Put them back in the freezer for another 10 minutes and re-coat them with butter. Put the pans back in the freezer until you are ready to bake your madeleines.
Preheat your oven to 385°F
After the madeleine batter has chilled for 60 minutes, remove it from the refrigerator and a butter-coated pan from the freezer. Using a generous tablespoon, fill each cavity with a dollop of batter. I have a 1½ tablespoon that works perfectly.
Bake for 10-11 minutes until the edges are just browned.