Preheat oven to 325 degrees F. Brush madeline pans well with 4 tablespoons of softened butter; refrigerate 5 minutes.
In a small heavy bottomed saucepan, melt 1/2 cup butter over medium heat. Remove from heat and strain through a fine mesh sieve into a small bowl; set aside.
In the bowl of an electric mixer fitted with the whisk attachment, whip eggs with granulated and brown sugars until light and thickened about 3 to 5 minutes. Add flour, cocoa powder, baking powder, and salt, and stir on low speed until combined. Add vanilla and strained butter; mix just until blended.
Use a teaspoon to fill the molds with batter. Bake until madeleines are firm and a little mound is puffed up in the middle about 12 minutes. Remove from pans to cooling rack
In a small heavy combine chocolate chips and vegetable shortening over medium-low heat. Melt stirring occasionally until all the chips are melted and mixture is smooth. Dip cooled cookies in melted chocolate, a few at a time. Sprinkle silver sprinkles from Sprinkle Pop over wet chocolate.