This fungus was growing on the broken beech. We previously identified it as black witches’ butter (Exidia glandulosa) or possibly Exidia plana (which prefers beech to oak).
Now we’re thinking policeman’s buttons (Bulgaria inquinans) as further outbreaks of the fungus are showing the regular circular shapes and felt-like sides. Policeman’s buttons grow most commonly on oak but occasionally on other dead hardwoods.
They are considered inedible and possibly poisonous in the west but are apparently a delicacy in China. Don’t risk it!