Begin by adding the unsalted butter to a sauce pan and heating it over medium low heat until simmering. Stir the butter occasionally. The butter will bubble and as it is heated it will start to turn a light golden brown color. Once you see that it has turned brown and is giving off a slightly nutty scent, remove it from the heat. Transfer the butter to a heat-safe medium bowl. Cool it until it is room temperature but still liquid.
9 tablespoon (126 g) unsalted butter
In a small bowl whisk together the all purpose flour, cocoa powder, baking powder and salt. Set aside the flour mixture.
1 cup (125 g) all purpose flour, spooned and leveled, 3 tablespoon (15 g) cocoa powder, ½ teaspoon baking powder, ¼ teaspoon salt
Add the granulated sugar, eggs and vanilla to a large bowl. Beat the eggs and sugar on high with an electric mixer for 3-5 minutes, or until the mixture is pale yellow and shiny. (This step helps to ensure the tops of the madeleines dome properly.)
⅔ cup (134 g) granulated white sugar, 2 large eggs, 1 teaspoon vanilla
Fold in the dry ingredients with a rubber spatula until everything is combined.
Pour in the cooled but liquid brown butter and fold it in just until combined. Don't over mix the batter.
Cover the bowl with plastic wrap and chill the batter in the fridge for 30 minutes.
Preheat the oven to 350 degrees. Use a pastry brush to brush melted butter into each madeleine well.
1 tablespoon melted butter
Add about 1 ½ tablespoon of batter into each well of the buttered pan.
Bake the madeleines for 9-11 minutes, until they have domed. Remove them from the oven and let them cool in their pan for a 5 minutes, then transfer them to a wire rack to completely cool.