Custom triggers on email templates

Is there a way to create an email that is sent to the site Admin that is triggered by an action I define myself?

Instead of using the default triggers (for example: New User Notification) I want to define a trigger. I would like to add a button to the Edit User Profile Page that says “Step 1 Approved” When the user clicks the button, I want the action on the button to be that it sends an email to the Admin. The email would say: “User X Approved Step 1.”

Thanks,
Paul