Place the beef mince, onion, grated vegetables, panko breadcrumbs, garlic, egg, parsley, tomato sauce, barbecue sauce, salt and pepper into a large bowl. Using clean hands or a spoon, mix gently until just combined — avoid over-mixing, as this can make the rissoles tough.
Divide the mixture into 8 equal portions and shape into rissoles about 2–3 cm thick. Place on a tray, cover and refrigerate if not cooking straight away (chilling helps them hold their shape).
Heat the oil in a large frying pan over medium heat. Working in batches, cook the rissoles for 5–6 minutes per side, or until golden brown and cooked through. Adjust the heat as needed to prevent burning. (For an easier option, cook the rissoles until just golden on each side then transfer the partially cooked rissoles to a lined oven tray and finish cooking in a 200°C (180°C fan) oven for 15-20 minutes)
Transfer cooked rissoles to a plate and repeat with the remaining mixture. Serve hot with mashed potato or oven-baked chips, steamed vegetables or salad, and tomato sauce or gravy.