You could try moving all his stacked dishes to the space where he wants to do something with a suggestion that it is better to put them in the dishwasher directly and not clutter up a space intended to work on?
You could stand in front of the still-messy cooker when it is time to make his next meal and refuse to cook anything on it until it is clean because it will just burn on permanently? Before he cleans it, of course, not you. Does he know how to? If not, it is time for a lesson. It is not rocket science.
You could leave the cooker dirty next time you use because, clearly, he believes that whoever cooks is let off cleaning duty.
And he is wrong, it does not stick because there is too little oil, but because he has the heat too high, or is clumsy turning things.