Melt butter in a large saucepan over medium heat. Remove from heat. Stir sugar into saucepan until dissolved. Add eggs and coffee liqueur; mix well to combine.
Sift flour, cocoa powder, and baking powder together in a large bowl. Stir into butter mixture until well-mixed and batter is stiff.
Preheat pizzelle baker according to manufacturer's instructions.
Drop spoonfuls of batter onto the preheated pizzelle baker. Bake until browned, about 45 seconds. Remove from baker and trim any ragged edges with scissors.
