Step 1Steam kumara and carrots in a microwave or on stove top for 8-10 minutes or until tender. Transfer vegetables to a large bowl, mash lightly and set aside.
Step 2Meanwhile, heat half of the oil in a small non-stick frying pan set over a medium heat. Add onion to pan. Cook for 2 minutes or until almost soft. Add curry paste and cook for 2 more minutes. Add baked beans. Simmer for 5 minutes or until sauce becomes thick and sticky, stirring regularly to stop sauce from burning. Remove pan from heat and leave sauce to cool for 5 minutes.
Step 3Stir baked-bean sauce into reserved vegetable mash. Add egg and breadcrumbs. Mix well.
Step 4Heat remaining oil in a large, shallow non-stick frying pan set over a low heat. Wet hands and shape bean mixture into 4 large patties, smoothing edges with a spoon (patties will be quite soft).
Step 5Cook patties in pan, flipping carefully, for 4 minutes each side or until patties are golden brown and heated through.
Step 6Mix yoghurt and cumin in a small bowl. Fill each roll with radicchio, cucumber ribbons, 1 bean pattie and a spoonful of yoghurt-cumin mixture. Serve.