Cordial Miners are a family of efficient Byzantine Atomic Broadcast protocols, with optimal instances for asynchrony and eventual synchrony. Their efficiency -- almost half the latency of state-of-the-art DAG-based protocols -- stems from not using reliable broadcast as a building block. Rather, Cordial Miners use the blocklace -- a partially-ordered generalization of the totally-ordered blockchain -- for all algorithmic tasks required for ordering consensus: Dissemination, equivocation-exclusion, and ordering.