Joel Varty describes the process of transitioning the Agility CMS website to a JAMstack architecture, specifically using Gatsby to build a new homepage while maintaining the existing ASP.NET Core framework for other pages. He emphasizes the benefits of using a headless CMS, which allows for content reuse and zero downtime during the transition. The project involved creating new modules and leveraging Agility CMS and Gatsby's capabilities for hot reloading and content synchronization. Varty outlines a step-by-step approach, from local development in Gatsby to deployment on platforms like Netlify and StackPath for CDN and edge routing. He highlights the flexibility and efficiency of the JAMstack approach, encouraging others to adopt similar strategies for their web projects, with additional support available through Agility CMS and Gatsby.