This paper presents BBCA-LEDGER, a Byzantine log replication technology for partially synchronous networks enabling blocks to be broadcast in parallel, such that each broadcast is finalized independently and instantaneously into an individual slot in the log. Every finalized broadcast is eventually committed to the total ordering, so that all network bandwidth has utility in disseminating blocks. Finalizing log slots in parallel achieves both high throughput and low latency. BBCA-LEDGER is composed of two principal protocols that interweave together, a low-latency/high-throughput happy path, and a high-throughput DAG-based fallback path. The happy path employs a novel primitive called BBCA, a consistent broadcast enforcing unique slot numbering. In steady state, BBCA ensures that a transaction can be committed with low latency, in just 3 network steps. Under network partitions or faults, we harness recent advances in BFT and build a fallback mechanism on a direct acyclic graph (DAG) created by BBCA broadcasts. In this manner, BBCA-LEDGER exhibits the throughput benefits of DAG-based BFT in face of gaps.