Ensemble learning is a meta-learning approach that combines the predictions of multiple learners, demonstrating improved accuracy and robustness. Nevertheless, ensembling models like Convolutional Neural Networks (CNNs) result in high memory and computing overhead, preventing their deployment in embedded systems. These devices are usually equipped with small batteries that provide power supply and might include energy-harvesting modules that extract energy from the environment. In this work, we propose E-QUARTIC, a novel Energy Efficient Edge Ensembling framework to build ensembles of CNNs targeting Artificial Intelligence (AI)-based embedded systems. Our design outperforms single-instance CNN baselines and state-of-the-art edge AI solutions, improving accuracy and adapting to varying energy conditions while maintaining similar memory requirements. Then, we leverage the multi-CNN structure of the designed ensemble to implement an energy-aware model selection policy in energy-harvesting AI systems. We show that our solution outperforms the state-of-the-art by reducing system failure rate by up to 40% while ensuring higher average output qualities. Ultimately, we show that the proposed design enables concurrent on-device training and high-quality inference execution at the edge, limiting the performance and energy overheads to less than 0.04%.