Continue screen recording even after screen turns off

I was screen recording with my iPad Pro and in the middle of it, I accidentally turned off my screen. I finished what I was doing and wanted to stop the screen recording but to my surprise it was already off.

I checked the resulting video and I only recorded up to the time I accidentally turned off my screen.

Is there a way for me to instruct the screen recorder to continue recording even when the screen is off?

No

There are no options for screen recording in the settings app. You also get a little notification that the recording has been stopped after you set the device to sleep.

If you own a Mac you could use QuickTime player to record the screen. Connect your device to the Mac with a cable then open QuickTime Player, right click on the icon in dock, select new recording and set the input to your mobile device (small arrow next to the red record-button). Then click record. It will continue the recording even though you set the mobile device to sleep.