JBoss Developer framework comes with TicketMonster, a moderately complex application that demonstrates how to build modern applications using JBoss web technologies. You can try using it, download it, fork it on GitHub and learn more about it from the accompanying tutorial.
Apart from being a demo, Ticket Monster provides an already existing application structure that you can grab and use for trying out your use cases, testing your own ideas, or, if you so wish, contribute back to the community with extensions.
Setup your project, leveraging Eclipse via JBoss Developer Studio, touching on JPA, JAX-RS, HTML5 and jQuery Mobile to get you started on using Java EE6 and JBoss.
Learn how to build the persistence layer for an application, and how to test it
Learn how to design and implement the business layer of an application and how to make it usable by various front-ends
Learn how to build the user interface in desktop and mobile version
Leverage JBoss Forge for rapid application development using AngularJS
Learn how to create hybrid mobile versions of the application with Apache Cordova