Electroencephalogram (EEG) emotion recognition faces challenges due to the non-Euclidean nature and nonlinear dynamics of EEG signals. Broad learning systems (BLSs), known for fast training and feature expansion, show significant potential in this domain. However, their design limits adaptation to graph-structured EEG data. To address this, a novel framework is introduced, combining BLS with graph convolutional networks (GCNs), realized as GCB-net and Residual GCB-net. BLS drives efficient feature expansion, while GCN modules enhance spatial-temporal feature extraction and model nonlinear EEG dynamics. Residual GCB-net incorporates identity mappings, enabling stable deep network training. Achieving state-of-the-art accuracies of 94.56% on SEED, 91.55% on DREAMER, and 72.20% on MPED, this approach demonstrates resilience to noise and individual variability. This research establishes BLS as a cornerstone for EEG emotion recognition, advancing its application and integration with graph-based models for complex signal analysis. Furthermore, the integration of BLS with GCN offers a promising avenue for the development of more efficient and robust emotion recognition systems, with potential applications in brain-computer interfaces and mental health monitoring.