The most efficient asynchronous Byzantine fault tolerant (BFT) framework innagreement settings is due to Ben-Or, Kemler, and Rabin (BKR), wherenis the total number of replicas. Despite recent efforts to bring BKR closer to practical deployment, state-of-the-art designs are still hampered by the inherent mutual waiting between the broadcast and agreement phases. In response, we propose ByzTopia, a new asynchronous BFT protocol that removes this performance bottleneck. Its technical core is to decouple these two phases without introducing additional cryptographic primitives. To enable a more efficient decoupling of the broadcast and agreement phases, we introduce multi-shot reliable broadcast (MRBC), which ensures that replicas deliver messages in a well-ordered sequence across consecutive slots. We implement ByzTopia and evaluate it in various settings. Experimental results show that ByzTopia achieves up to 6.54× the throughput of PACE (for n == 31), the state-of-the-art asynchronous BFT of the same type, and 2.65× that of FIN (for n = 16), the state-of-the-art signature-free asynchronous BFT.