This article proposes a new Artificial Intelligent (AI) and Machine Learning (ML) based framework for 6G-enabled Intelligent edge computing. The framework will be equipped with multiple cognitive controllers to harmoniously control various aspects in distributed intelligence toward edge nodes collaboration. Autonomic cognitive controller for edge computing is a popular computing paradigm where the distributed metadata processing and edge intelligence are performed at edge node in 5G/6G network for management, connectivity and interoperability. Some of studies focused on edge management improvement such as reduce the response time and bandwidth costs. However, the previous approaches are inadequate to support autonomously management for large-scale deployment for connectivity for dynamic and reliable communication. We propose a cognitive controller for edge autonomy and collaboration application development. Finally, we discuss challenges and open issues toward cognitive controller and distributed edge intelligence.