The prevailing AI paradigm, grounded in the Turing model, operationalizes intelligence as symbol manipulation and scales performance through parameter growth and stochastic optimization. While this approach underlies deep learning and large language models, its reliance on brute-force computation imposes severe energy and epistemic costs: training a single foundation model such as GPT-3 requires over 1,200 MWh, and inference at scale accelerates unsustainable data-center expansion. Moreover, statistical generalization without semantic grounding limits interpretability and adaptability. This paper proposes Mindful Machines as a post-Turing, knowledge-centric alternative to computation-centric architectures. Mindful Machines integrate three interdependent layers—physical embodiment for environmental coupling, representational structures for symbolic and sub-symbolic integration, and reflective mechanisms for self-regulation and autopoiesis. This architecture enables adaptive knowledge reuse, goal-driven learning, and dynamic constraint satisfaction, reducing retraining overhead while enhancing semantic depth. By formalizing cognition as a triadic system rather than a unidimensional computational process, we demonstrate how meaning-driven architectures can achieve functional scalability with significantly lower energy budgets. The results suggest a paradigm shift toward sustainable AGI, where intelligence emerges from structured interaction and self-maintenance rather than parameter escalation.