“I can cook,” said Sophie. “Unhook that frying pan and I’ll show you.”
“She reached for the large black pan hanging on the closet wall, in spite of Michael trying to prevent her. “You don’t understand,” Michael said. “It’s Calcifer, the fire demon. He won’t bend down his head to be cooked on for anyone but Howl.”
Sophie turned and looked at the fire demon. He flickered back at her wickedly. “I refuse to be exploited,” he said. (Howl’s Moving Castle, by Diana Wynne Jones)
What does ‘to be cooked on’ mean?
While eggs and bacon can be cooked on the frying pan with the fire, how the fire could be cooked? And what role does ‘on’ take? Is there an omission of subject for ‘to be cooked’: e.g. eggs and bacon? And is there the invisible complement of ‘on’: his head?