The advancement of automatic speech recognition (ASR) has been largely enhanced by extensive datasets in high-resource languages, while languages such as Hungarian remain underrepresented due to limited spontaneous and conversational corpora. To address this gap, we introduce two new datasets -- BEA-Large and BEA-Dialogue -- constructed from the previously unprocessed portions of the Hungarian speech corpus named BEA. BEA-Large extends BEA-Base with 255 hours of spontaneous speech from 433 speakers, enriched with detailed segment-level metadata. BEA-Dialogue, comprising 85 hours of spontaneous conversations, is a Hungarian speech corpus featuring natural dialogues partitioned into speaker-independent subsets, supporting research in conversational ASR and speaker diarization. We establish reproducible baselines on these datasets using publicly available ASR models, with the fine-tuned Fast Conformer model achieving word error rates as low as 14.18% on spontaneous and 4.8% on repeated speech. Diarization experiments yield diarization error rates between 12.46% and 17.40%, providing reference points for future improvements. The results highlight the persistent difficulty of conversational ASR, particularly due to disfluencies, overlaps, and informal speech patterns. By releasing these datasets and baselines, we aim to advance Hungarian speech technology and offer a methodological framework for developing spontaneous and conversational benchmarks in other languages.