In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs and sugar together on medium-high speed until they are smooth, pale yellow, and creamy, about 8 minutes.

Using a rubber spatula, gently fold the flour, pumpkin puree, pumpkin pie spice, and baking powder into the creamed mixture.

Add the melted and cooled butter (it should still be liquid, but not warm to the touch). Fold the butter into the batter gently.

Transfer the batter to the refrigerator to chill for 30 minutes.

Toward the end of the chilling step, preheat the oven to 350 degrees F. Grease a madeleine pan with melted butter and nonstick spray.

Scoop 1 tablespoon of batter into each mold, making sure to fill each one about 3/4 of the way full.

Bake in a preheated oven until the madeleines are light brown and a toothpick inserted into the center comes out clean, about 10-12 minutes.

Transfer the madeleines to a wire rack to cool.

Once cool, dip the cookies in the melted white chocolate.