Anthony Giuliano's tutorial explores building cross-platform components using Stencil and Capacitor, focusing on creating a versatile avatar component that functions across web and mobile platforms. The tutorial emphasizes the limitations of traditional web design systems that overlook mobile compatibility and demonstrates how to overcome this by using Stencil, a web components compiler, and Capacitor, a cross-platform native runtime. By developing an avatar component that allows users to change their avatar images through file selection on the web or via the camera and photo library on mobile devices, Giuliano showcases the potential for creating flexible design systems that maintain consistency and feature parity across different platforms. The tutorial includes detailed steps for integrating Capacitor, utilizing the Capacitor Camera Plugin, and enhancing the component's API with custom events, demonstrating how these technologies facilitate the creation of unified design systems suitable for varied applications.