Just bought a brand new iPhone 13 and it has now randomly restarted about a dozen times

Take a Backup either on iCloud after enabling all iCloud Options ((Preferable) or iTunes (Encrypted).

Settings > General > Reset > Erase All Content & Settings > [Do not keep anything on the device]

If you are given the option to Erase and Erase and Keep Data Plan (Dual SIM) Then Select Erase and Keep Data Plan

Set it up as a new device and check if the same issue recurs, probably it won't.

• If it does then you need to take your device for repair or service
• If it doesn't, then there is no issue with the device. Restoring from the backup may bring the issue back.
• Set it up as a new device and use iCloud and bring back synced data in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, Messages*, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.
• Download all Apps from the App Store one by one especially those which did not have any App Data stored on your device

Please follow the steps in the following link for support with this issue: If your iOS device restarts or displays the Apple logo or a spinning gear unexpectedly

mm48452 wrote:

I have looked at support forums and it suggests looking at whether a panic-base file is created.

Please don't go by hearsay.