Make the batter the night before or up to three days ahead.
Melt 13 tablespoon of the butter in a small sauce pan and set aside to cool.
In a large mixing bowl, combine the eggs and sugar and use a whisk to beat them together for a minute or two until light and frothy. Then whisk in the milk.
Sift the flour, baking powder, and baking soda into another large bowl. Whisk in the tea and salt and stir to combine.
Add dry ingredients into the wet ingredients a little at a time and whisk together gently.
Then add the melted butter and whisk until it is fully incorporated and you have a smooth shiny batter. You'll know the batter is right when it falls from your whisk in wide, flat ribbons. Cover the batter tightly and refrigerate overnight or up to three days.
Use a tablespoon to scoop the batter into each madeleine mold, filling about ¾ full. And I don't mean use a measuring spoon that equals 1 tablespoon. I mean an actual tablespoon. The kind you find in your silverware drawer next to the forks. You can spread the batter out a little with your fingers if need be, but don't mush it down. Remember the batter needs to stay cold so handle it as little as possible.
Place the pan in the center rack of the oven and bake for 10-13 minutes, until the madeleine has a nice bump and is golden brown around the edges. Put the remaining batter back in the refrigerator.
To get the madeleines out of the pan, grasp it with both hands and tilt so they are facing away from you while banging the bottom edge of the pan on the counter and they will pop out. It might take a couple of tries to get them all. Place them on a rack to cool.
Allow the pan to come to room temperature before you fill it up with batter again. Which could be right away or could be tomorrow. Remember the batter lasts a few days.
Season the pan - coat the molds with melted butter, then wipe clean with a paper towel, and coat them again.
Sift the flour for fluffy madeleines! (also the baking powder and baking soda to avoid lumps)
Keep the batter in the fridge in between batches
Do a test bake with 2-4 madeleines in the molds. This helps you make sure that the amount of batter and the amount of baking time is just right before baking a whole pan full.
Allow the pan to come to a cool room temperature before baking the next batch. Like, don't let it cool next to the oven. Move it to the next room over away from the kitchen and wave it around if you have to. (I did.)
It seems like the tea makes these look a little darker than they really are on the bottom. I tested with and without the tea, the ones with tea looked darker, but didn't actually taste like they were baked too long.
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