Understanding how the brain encodes and reconstructs sound is central to hearing science and clinical audiology. Traditional EEG decoding methods, such as the envelope following response, have revealed important aspects of neural speech tracking but remain limited by their linear assumptions and restricted sound representations. These approaches capture only part of the complex, non-linear neural dynamics that support natural sound perception. Here, we introduce a new framework that applies a Large Language Model (LLM) architecture to decode EEG signals and reconstruct the corresponding sound. We adapted a pre-trained NeuroLM model - derived from GPT-2 and trained on large-scale EEG datasets -to predict neural representations of acoustic tokens. EEG signals from the SparrKULee dataset (105 normal-hearing participants, 64-channel recordings during audiobook and podcast listening) were converted into discrete “EEG tokens,” while the associated stimuli were tokenized using an EnCodec model at bitrates from 1.5 to 6 kbps. NeuroLM variants (254 M to1.7 B parameters) were fine-tuned to map EEG sequences to sound tokens, enabling continuous audio reconstruction from neural activity. Reconstructed signals were assessed using objective acoustic measures (mel-spectrogram correlation, PESQ, phase coherence) and subjective tests (intelligibility and MUSHRA ratings). The best-performing models produced intelligible and perceptually recognisable reconstructions, even for participants unseen during training. Beyond its methodological innovation, this work highlights the potential of LLM-based neural decoding as a clinical research tool. This approach could help evaluate and refine hearing technologies and investigate how individual factors - such as electrode placement or neural health - shape cortical representations of speech in cochlear implant (CI) users. It may also reveal how CI users compensate for degraded information or support EEG-based diagnostics, advancing understanding of auditory perception in both typical and impaired hearing.