iPhone 11 won't connect to Bluetooth headphones

You are not addressing Apple here. This is a user to user support forum and Apple does not participate here. Have you made sure that the Headphones are in discovery/pairing mode? They need to be in that state for the iPhone Bluetooth to "see" them. You can also check this support document for assistance with connecting Bluetooth devices. If you can't connect a Bluetooth accessory to your iPhone, iPad, or iPod touch - Apple Support

Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch - Apple Support

Make sure each device you are trying to pair is in "discoverable mode"

Control Center - tap bluetooth off and on again - 8-10 times

Force restart the iPhone - After shutting down all open apps using the app switcher - invoked by quick double press of the home button and swiping up on each app till it flies off the screen. Hold the sleep/wake and home buttons down together till you see  logo - then release and allow normal boot up

Update to the latest iOS if not done 

Settings -General - Reset - Reset Network settings will need to re enter WiFi passwords

If Apple pencil is connected - "Forget it" and try again

Backup the device to iTunes - Restore as NEW (not from backup) - see if problem resolves - if yes - restore backup

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider.