In this paper, a green learning (GL)-based precoding framework is proposed for simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided millimeter-wave (mmWave) MIMO broadcasting systems. Motivated by the growing emphasis on environmental sustainability in future 6G networks, this work adopts a broadcasting transmission architecture for scenarios where multiple users share identical information, improving spectral efficiency and reducing redundant transmissions and power consumption. Different from conventional optimization methods, such as block coordinate descent (BCD) that require perfect channel state information (CSI) and iterative computation, the proposed GL framework operates directly on received uplink pilot signals without explicit CSI estimation. Unlike deep learning (DL) approaches that require CSI-based labels for training, the proposed GL approach also avoids deep neural networks and backpropagation, leading to a more lightweight design. Although the proposed GL framework is trained with supervision generated by BCD under full CSI, inference is performed in a fully CSI-free manner. The proposed GL integrates subspace approximation with adjusted bias (Saab), relevant feature test (RFT)-based supervised feature selection, and eXtreme gradient boosting (XGBoost)-based decision learning to jointly predict the STAR-RIS coefficients and transmit precoder. Simulation results show that the proposed GL approach achieves competitive spectral efficiency compared to BCD and DL-based models, while reducing floating-point operations (FLOPs) by over four orders of magnitude. These advantages make the proposed GL approach highly suitable for real-time deployment in energy- and hardware-constrained broadcasting scenarios.