Despite the rapid progress of Vision-Language Models (VLMs), the field lacks benchmarks that rigorously diagnose their true reasoning abilities and chart meaningful progress toward human-like multimodal intelligence. Most existing evaluations focus on piecemeal or disconnected tasks, obscuring critical cognitive weaknesses and providing little insight for targeted improvement. To address this gap, we introduce BloomBench, part of the Almieyar benchmarking series, the first cognitively human-grounded, bilingual (English-Arabic) multimodal benchmark for VLMs. Grounded in Bloom's Taxonomy, BloomBench systematically evaluates six levels of cognition (Remember, Understand, Apply, Analyze, Evaluate, Create) through carefully designed image-question-answer tasks. Built with a semi-automated pipeline and validated through a stratified hybrid quality assurance protocol, it ensures scalability, cultural inclusivity, and linguistic fidelity. Leveraging this framework, we conduct a comprehensive study of state-of-the-art VLMs to diagnose their cognitive profiles. Our analysis reveals a sharp cognitive asymmetry: while state-of-the-art models achieve strong performance ceilings in semantic understanding, they struggle substantially with factual recall and creative synthesis. This demonstrates that current general multimodal proficiency masks deeper limitations in specific cognitive layers. Furthermore, our study highlights a critical performance gap between Arabic and English, exposing limitations in current cross-lingual multimodal reasoning. These findings establish a foundation for developing more cognitively aligned and inclusive VLMs. The benchmark framework and dataset is available at: https://github.com/qcri/Almieyar-Oryx-BloomBench.