In the bowl of a stand mixer using the whisk attachment, beat eggs and granulated sugar until frothy and thickened, about 2 minutes. Add pumpkin, zest, and vanilla and beat until incorporated. Remove bowl from mixer.
In another bowl, mix flour, baking powder, cinnamon, salt, cloves, and nutmeg. Using a rubber spatula, fold flour mixture into egg mixture.
Fold 1/2 cup melted butter, a few spoonfuls at a time, into batter. Fold just until butter is incorporated. Chill at least 1 hour and up to 12 hours.
Preheat oven to 425°. Brush molds of 2 madeleine pans with melted butter.
Using a small spoon, fill each mold about 3/4 full with batter and spread to edge of mold. Bake until edges are golden brown, about 9 minutes.
Meanwhile, melt white chocolate and coconut oil in a bowl set over (not in) 1 in. simmering water in a saucepan.
Make icing: In a small bowl, mix 1 cup powdered sugar with milk. Add enough food coloring to make it deep black. The icing should be fluid enough to pipe, but not runny. If it's runny, add more powdered sugar, 1 tbsp. at a time; if it's too thick, add milk, 1 tsp. at a time. Spoon icing into a small resealable plastic bag.
Let madeleines cool in molds 2 minutes. Line a baking pan with parchment. Using an offset spatula, lift madeleines out to a cooling rack. The moment they're cool enough to handle, dip curved top half of each in melted white chocolate and set, ridged side up, on parchment-lined pan. Set edible eyes toward top of chocolate-dipped half.
Freeze pan of madeleines for a few minutes to set chocolate. Squish icing into a corner of bag, then cut off just the tip of corner to create a piping bag. Pipe mouths onto madeleines (practice on parchment first).
*Find black food coloring and candy eyeballs in the baking aisle of well-stocked grocery stores.