In a mixing bowl, whisk together eggs and sugar thoroughly combined and pale yellow. Whisk in melted butter, cocoa powder, evaporated milk, and coffee liqueur. Set aside.
Place pie shell on baking sheet and place on an oven rack. Carefully pour in filling. Bake in preheated oven for 45 minutes. About 5 minutes before pie is finished, mound marshmallows in the center of the pie (they will spread as they melt). Continue baking until marshmallows are golden brown.