In a Laravel application, sending periodic emails using Twilio SendGrid is made possible by creating a custom artisan command that schedules the task. To achieve this, first install the necessary packages and set up the database for the application. Next, create a Seeder class to populate the users table with sample data. Then, create a new Console command class to send out emails using the SendGrid SDK. Finally, schedule the command to run daily or at any desired frequency using the `schedule()` method in the Kernel class. The process involves several steps, including setting up the database, creating the Seeder class, defining the custom artisan command, and scheduling it to run. After completing these steps, the application can send out periodic emails to registered users.