Building a new Parse Server and MongoDB Atlas-based application involves deploying a MongoDB Atlas cluster, creating a user with readWrite access to the database, and configuring Parse Server to connect to the MongoDB Atlas backend. The process can be automated using tools such as AWS Elastic Beanstalk or Heroku, which provide easier set-ups than others. Once the configuration is complete, the Parse Server application can be tested using curl commands to confirm connectivity. With a MongoDB Atlas cluster in place, developers can now build new applications pointing to their instance of Parse Server and MongoDB Atlas, taking advantage of the benefits of cloud-based infrastructure and scalable storage.