Spray a Madeleine pan with non-stick cooking spray and set aside.
In the bowl of an electric mixer, fitted with the whisk attachment, combine the flour, eggs, salt and baking powder. Whip on high speed until thick, about 3 minutes. Turn mixer to low speed and continue mixing. Slowly add butter and sugar, whipping another 2 minutes until mixture is thick and creamy. Fold in pumpkin puree with a rubber spatula until just mixed. Stirring just enough to incorporate.
Spoon the batter into the molds, filling each well about 2/3 full. Bake for 12 to 14 minutes or until the edges are golden brown. Remove from oven and unmold immediately. If you need to use the same madeleine pan for the balance of the batter, wash, dry and repeat with non-stick spray. If you just fill with more batter, the madeleines will stick a bit.