Information retrieval systems have historically relied on explicit query formulation, requiring users to translate their information needs into text. This process is particularly disruptive during reading tasks, where users must interrupt their natural flow to formulate queries. We present DEEPER (Dense Electroencephalography Passage Retrieval), a novel framework that enables direct retrieval of relevant passages from users' neural signals during naturalistic reading without intermediate text translation. Building on dense retrieval architectures, DEEPER employs a dual-encoder approach with specialised components for processing neural data, mapping EEG signals and text passages into a shared semantic space. Through careful architecture design and cross-modal negative sampling strategies, our model learns to align neural patterns with their corresponding textual content. Experimental results on the ZuCo dataset demonstrate that direct brain-to-passage retrieval significantly outperforms current EEG-to-text baselines, achieving a 571% improvement in Precision@1. Our ablation studies reveal that the model successfully learns aligned representations between EEG and text modalities (0.29 cosine similarity), while our hard negative sampling strategy contributes to overall performance increases.