Rob Spectre from Twilio shares his experience building a mustachify service using Twilio's MMS and Python, inspired by Aidan Feldman's original Mustachify.me service. The project starts with setting up a Flask app, importing necessary libraries, and defining an endpoint for receiving Twilio SMS messages. Once the basic endpoint is created, a Twilio phone number is configured to point to it, allowing users to send messages that will be echoed back with a response containing the original message's media, such as photos or images. The project then uses Aidan's mustachify.me service to apply a mustache effect to the received image, creating a "stashed" face. The code is made available for developers to build upon, and Twilio encourages users to share their own MMS hacks and ideas for further developing this technology.