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Melt the butter in a small frying pan, add the onion and cook on a medium heat until soft and translucent, then cool. Tip the pork into a large bowl and add the onion, egg yolks and thyme. Season well and mix together with your hands – don’t overhandle or you will make the burgers tough. Divide the mixture into 4 and shape into burgers. Chill for 30 mins to firm up.
Heat the barbecue and cook the burgers for 10 mins each side. Top each burger with a slice of cheese, followed by 1 tbsp apple sauce, then return to the barbecue and close the lid, cooking for a further 5 mins to allow the cheese to melt. If your barbecue doesn’t have a lid, loosely cover with foil.
Quickly toast the buns, then serve with the burgers and some salad leaves inside.