Ajax request from frontend of custom module

Without Ajax, how will I asynchronously populate the calendar when a user selects a new month, day or year?

The page loads, displaying the current month - I can pre-populate that… but I need Ajax to update it. It is a pattern I have used before - placing the the methods called by my client side ajax function within functions.php (I’m a novice with wordpress and PHP. I’m a Node and Elixir developer for the day job).

Rather than place the methods inside functions.php - I wanted to include them within the custom Beaver Builder plugin so that they are protected against updates.