Mix cooled coffee and Marsala wine together in a bowl.
Beat egg yolks with half of the sugar in a bowl until you have a clear cream with no lumps. Stir the mascarpone with a wooden spoon or whisk in a separate bowl until creamy; stir into the egg yolks.
Beat the egg whites with the remaining sugar in a separate bowl using an electric mixer until they form peaks; fold gently into mascarpone mixture.
Dip half of the savoiardi biscuits into coffee-Marsala mixture. Arrange dipped biscuits carefully in a glass dish. Cover dipped biscuits with half of the mascarpone mixture. Smooth out mascarpone until evenly distributed; top with half of the cocoa powder. Repeat layering with dipped savoiardi biscuits, mascarpone mixture, and cocoa powder; top with chocolate shavings.
Refrigerate tiramisu until flavors blend, at least 3 hours.