Large Language Models (LLMs) face a fundamental challenge in deciding when to rely on rapid, intuitive responses versus engaging in slower, more deliberate reasoning. Inspired by Daniel Kahneman's dual-process theory and his insights on human cognitive biases, we propose a novel Cognitive Decision Routing (CDR) framework that dynamically determines the appropriate reasoning strategy based on query characteristics. Our approach addresses the current limitations where models either apply uniform reasoning depth or rely on computationally expensive methods for all queries. We introduce a meta-cognitive layer that analyzes query complexity through multiple dimensions: correlation strength between given information and required conclusions, domain boundary crossings, stakeholder multiplicity, and uncertainty levels. Through extensive experiments on diverse reasoning tasks, we demonstrate that CDR achieves superior performance while reducing computational costs by 34\% compared to uniform deep reasoning approaches. Our framework shows particular strength in professional judgment tasks, achieving 23\% improvement in consistency and 18\% better accuracy on expert-level evaluations. This work bridges cognitive science principles with practical AI system design, offering a principled approach to adaptive reasoning in LLMs.