Add butter to a heavy saucepan, and cook over a medium heat, stirring constantly. Cook until the butter foams, turns clear, and then medium brown. Pour the browned butter into a glass measuring cup and allow to cool for 10 minutes.

In a medium bowl combine the flour, white sugar, brown sugar, pecans, and baking soda. Set aside.

In a small mixing bowl combine eggs, and vanilla and whisk until frothy, about 1 minute.

Add the egg mixture to the flour mixture and stir with a rubber spatula until just combined. Add the cooled brown butter and stir until just combined, without over mixing. Cover the bowl and let the madeleine batter rest in the fridge for an hour, or upto overnight.

Preheat the oven to 350 and spray a madeleine tin with cooking spray. Fill the molds with a generous tablespoon of batter. Bake about 14 minutes, until the madeleines are puffed and golden, and spring back from the edges when touched. Remove from the pan and cool on a wire rack. Dust with confectioner's sugar before serving.