Put a third of the grated carrot in a food processor with the mash, 2 tbsp tahini, cumin and egg.
Whizz to a thick paste, then scrape into a large bowl. Heat 1 tbsp oil in your largest frying pan, tip in the remaining carrot and cook for 8-10 mins, stirring until the carrot is softened – it will become more golden as it is cooked.
Add this cooked carrot to the whizzed paste with the gluten free breadcrumbs, lemon zest and sesame seeds. Add seasoning, then mix together well with your hands.
Divide the mixture into 6, then using wet hands shape into burgers.
Cover and chill until serving. Mix the lactose free yogurt with the remaining tahini and lemon juice, then chill.
Fire up the barbecue, or heat a non-stick frying pan and brush the burgers with the remaining oil.
Cook the burgers for 5 mins on each side, until golden and crisp.