Accurate brain tumor classification is crucial in medical imaging to ensure reliable diagnosis and effective treatment planning. This study introduces a novel double ensembling framework that synergistically combines pre-trained deep learning (DL) models for feature extraction with optimized machine learning (ML) classifiers for robust classification. The framework incorporates comprehensive preprocessing and data augmentation of brain magnetic resonance images (MRI), followed by deep feature extraction using transfer learning with pre-trained Vision Transformer (ViT) networks. The novelty lies in the dual-level ensembling strategy: feature-level ensembling, which integrates deep features from the top-performing ViT models, and classifier-level ensembling, which aggregates predictions from hyperparameter-optimized ML classifiers. Experiments on two public Kaggle MRI brain tumor datasets demonstrate that this approach significantly surpasses state-of-the-art methods, underscoring the importance of feature and classifier fusion. The proposed methodology also highlights the critical roles of hyperparameter optimization (HPO) and advanced preprocessing techniques in improving diagnostic accuracy and reliability, advancing the integration of DL and ML for clinically relevant medical image analysis.