Conventional robotic Braille readers typically rely on discrete, character-by-character scanning, limiting reading speed and disrupting natural flow. Vision-based alternatives often require substantial computation, introduce latency, and degrade in real-world conditions. In this work, we present a high accuracy, real-time pipeline for continuous Braille recognition using Evetac, an open-source neuromorphic event-based tactile sensor. Unlike frame-based vision systems, the neuromorphic tactile modality directly encodes dynamic contact events during continuous sliding, closely emulating human finger-scanning strategies. Our approach combines spatiotemporal segmentation with a lightweight ResNet-based classifier to process sparse event streams, enabling robust character recognition across varying indentation depths and scanning speeds. The proposed system achieves near-perfect accuracy (>=98%) at standard depths, generalizes across multiple Braille board layouts, and maintains strong performance under fast scanning. On a physical Braille board containing daily-living vocabulary, the system attains over 90% word-level accuracy, demonstrating robustness to temporal compression effects that challenge conventional methods. These results position neuromorphic tactile sensing as a scalable, low latency solution for robotic Braille reading, with broader implications for tactile perception in assistive and robotic applications.