iPhone won't allow Bluetooth headphones on phone calls

iPhone 7 Plus running iOS 11.2.1. Using Bose QC35 II headphones running firmware version 2.1.3.

My iPhone will not allow me to use Bluetooth headphones to place or receive phone calls. Additionally, I cannot use Bluetooth headphones during a call.

Screencast of issue: http://ca.mag.cm/2j2A003K0U1L

When I begin a phone call and select the connected Bluetooth headphones (Bose QC 35 II) as the audio source, the Phone app will cease playing audio over the phone's speaker and makes some kind of attempt to transfer the audio to the headphones. However, I will not be able to hear any audio coming from the Bluetooth headphones and the person calling me will not be able to hear my voice coming from the headphone's microphone. After several seconds of trying to use the Bluetooth headphones as the audio source, the Phone app automatically switches back to using the iPhone as the audio source.

If I attempt to use a button on the headphones to answer the call, the call will be successfully answered but I won't hear any audio over the headphones and the person on the call will not be able to hear me for several seconds. After several seconds, the phone automatically switches the audio source from the Bluetooth headphones to the iPhone and I will be able to continue the call from there.

While I am able to use this pair of Bluetooth headphones normally with other apps such as Spotify, Pocket Casts, Siri, and Google Assistant, the Phone app seems to be unable to use Bluetooth headphones as an audio source.

To troubleshoot this issue, I have upgraded iOS from 11.2 to 11.2.1 as well as restarted the phone. I have also reproduced the issue with a different pair of Bluetooth headphones and the same problem occurs with the different pair.

Does anyone know why the Phone app refuses to use Bluetooth headphones as an audio source and how I can work through this issue?