In a medium bowl, whisk together the eggs, sugar and brown sugar. In another medium bowl, whisk together the all-purpose flour, baking powder and salt.
Sift the dry ingredients into the wet and mix until barely combined. Pour in the melted butter and mix once more until mostly smooth. Transfer the batter to a ziplock/plastic bag, pressing out any air, seal and transfer to the fridge to rest for at least 1 hour, up to 2 to 3 days.
Preheat the oven to 375 degrees F. If needed, grease and flour your madeleine pan. Cut off the end of the plastic bag and pipe the batter into each cavity, filling about 3/4 of the way (you may end up with two tablespoons of batter left).
Transfer to the oven to bake for 7 to 8 minutes, until edges are golden brown and centers are puffed and lightly spring back when gently pressed. Tap pan against counter to release. Dust with a liberal amount of powdered sugar and serve warm.
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