A Java developer creates a standalone voicemail system using Twilio and Apache Tomcat. The system receives incoming calls, records the caller's voice, and sends a text message with a link to listen to the recording. The project involves setting up an environment, creating servlets for handling incoming calls and sending outgoing messages, and configuring account credentials. The developer uses ngrok to make the server publicly accessible. The final application allows users to record voicemails without giving out their real number and can be customized for different types of calls.