Melt ½ cup of butter in a small saucepan over medium-low heat.  Cook, stirring constantly with a whisk until the butter starts to foam.

Keep whisking the butter and continue to cook until the butter takes on a deep golden brown color, has dark flecks, and smells nutty – about 5 minutes.

Remove the pan from the heat and allow it to cool.

In the bowl of a stand mixer with the paddle attachment, beat together the eggs and both brown and granulated sugars until smooth and creamy – about 8 minutes.

Add the pumpkin and beat until combined.

Use a spatula to fold in the flour, pumpkin pie spice, and baking powder.  Use a light touch.  We don’t want to develop too much gluten, which will toughen the cake.

Pour in the cooled, melted butter and fold into the mixture until well combined.

Cover the bowl tightly with plastic wrap and chill for 30 minutes.

Preheat the oven to 350 degrees.

Melt the remaining 2 tablespoons of butter and brush the insides of 2 madeleine pans.

Scoop 1 tablespoon of the batter into each mold, filling each one about ¾ of the way full.

Place the pans in the top ⅓ of the oven.

Bake in the preheated oven until the madeleines are golden brown and a toothpick inserted into the thickest part comes out clean – about 15 minutes.  Take care not to overbake.

Meanwhile, in a small bowl stir together the superfine sugar and cinnamon.

When the madeleines are done, flip the madeleine pan to remove the cookies or if necessary, use a spoon to gently unmold them.

While still warm, roll each madeleine in the sugar/cinnamon mixture.

Place on a wire rack to cool completely before serving.