Crack their cheeks

I don't understand what "crack their cheeks" means in the following sentence, taken from an article published in The Economist : "And since neither of them is a fool, both crack their cheeks trying to sound sympathetic."

I've never heard this either. I'm sure it's meant as sarcasm, perhaps like "He almost cracked his jaw trying to smile." But I don't know any standard facial gesture associated with sounding sympathetic, especially in regard to the cheeks. There are a several ways one can make sounds with one's mouth, including a sort of clucking using the cheeks. One or two of these sounds could be construed as sympathetic sounds. But I don't know what the author had in mind. Perhaps there is a British idiom, cracking one's cheeks.
SS

Not that it reveals the meaning very well for me, but there's a reference to this phrase in the archives here. It's a phrase from Shakespeare.

The missing link is below.