Adapted from Baking From My Home to Yours
(I don't have a Madeleine pan so I used a mini muffin pan.)
⅔ cup all-purpose flour
¾ teaspoon baking powder
Pinch of salt
½ cup sugar
Grated zest of 4 key limes
2 large eggs, at room temperature
1 teaspoon vanilla extract
1 teaspoon coconut extract
5 tablespoons light butter, melted and cooled
Confectioners' sugar, for dusting
Whisk together the flour, baking powder and salt.
Working in a mixer bowl, or in a large bowl, rub the sugar and key lime zest together with your fingertips until the sugar is moist and fragrant. Add the eggs to the bowl. Working with the whisk attachment, or with a hand mixer, beat the eggs and sugar together on medium-high speed until pale, thick and light, 2 to 3 minutes. Beat in the vanilla. With a rubber spatula, very gently fold in the dry ingredients, followed by the melted butter. Press a piece of plastic wrap against the surface of the batter and refrigerate it for at least 3 hours, or for up to 2 days. This long chill period will help the batter form the hump that is characteristic of madeleines. (For convenience, you can spoon the batter into the Madeleine molds, cover and refrigerate, then bake the cookies directly from the fridge; see below for instructions on prepping the pans.)
Center a rack in the oven and preheat the oven to 400 degrees F. Butter 12 full-size Madeleine molds, or up to 36 mini Madeleine molds, dust the insides with flour and tap out the excess. Or, if you have a nonstick pan (or pans), give it a light coating of vegetable cooking spray. If you have a silicone pan, no prep is needed. Place the pan(s) on a baking sheet.
Spoon the batter into the molds, filling each one almost to the top. Don't worry about spreading the batter evenly, the oven's heat will take care of that. Bake large madeleines for 11 to 13 minutes, and minis for 8 to 10 minutes, or until they are golden and the tops spring back when touched. Remove the pan(s) from the oven and release the madeleines from the molds by rapping the edge of the pan against the counter. Gently pry any recalcitrant madeleines from the pan using your fingers or a butter knife. Transfer the cookies to a rack to cool to just warm or to room temperature.
If you are making minis and have more batter, bake the next batch(es), making certain that you cool, then properly prepare the pan(s) before baking.
Just before serving, dust the madeleines with confectioners' sugar.