This paper presents a novel framework for joint speaker diarization (SD) and automatic speech recognition (ASR), named SLIDAR (sliding-window diarization-augmented recognition). SLIDAR can process arbitrary length inputs and can handle any number of speakers, effectively solving ``who spoke what, when'' concurrently. SLIDAR leverages a sliding window approach and consists of an end-to-end diarization-augmented speech transcription (E2E DAST) model which provides, locally, for each window: transcripts, diarization and speaker embeddings. The E2E DAST model is based on an encoder-decoder architecture and leverages recent techniques such as serialized output training and ``Whisper-style" prompting. The local outputs are then combined to get the final SD+ASR result by clustering the speaker embeddings to get global speaker identities. Experiments performed on monaural recordings from the AMI corpus confirm the effectiveness of the method in both close-talk and far-field speech scenarios.