BBCA-Chain is a novel consensus protocol designed for Directed Acyclic Graph (DAG) structures, aiming to simplify and enhance the efficiency of DAG-based consensus mechanisms. It leverages a new broadcast primitive called Byzantine Broadcast With Commit-Adopt (BBCA), which builds upon Byzantine Reliable Broadcast (BRB) to allow for single-broadcast consensus with reduced latency by minimizing network trips. BBCA-Chain's structure enables leader-blocks to be committed without additional votes or DAG layering, using BBCA to maintain a causally ordered sequence, while non-leader blocks are broadcast in parallel using a best-effort approach. This protocol addresses the limitations of existing DAG-based solutions by eliminating unnecessary latency and complexity typically associated with multiple broadcast layers. Through BBCA's Commit-Adopt API, nodes can efficiently lock and commit values, ensuring safety and consistency within the network. Compared to protocols like Bullshark, BBCA-Chain significantly reduces latency and communication steps, achieving optimal efficiency for Byzantine consensus without the need for structured DAG layering constraints.