Yes, but this would require some coding off your own.
The Management API allows you to request a Password Reset ticket. This is not the same as sending the reset email. The ticket is just the URL users need to visit to reset their password. So, here’s what you could do:
- Have a page where users enter their usernames
- Query the Management API for that user, get their secondary email
- Request a Password Reset ticket for that user ID
- Send a custom email to the secondary email
Sending that email doesn’t have to be hard, either. For our Auth0 deployment, we use SendGrid. They also provide a way to call their API and send an email with a predefined template (so you only have to send the email and ticket URL to the API). I’m sure other email providers allow you to do something similar.