1. To make the pickled onions, dissolve the sugar in boiling water in a bowl. Add the vinegar and onion and stir to combine. Allow to stand for 1 hour.
2. To make the beef patties, combine all the ingredients in a large bowl. Divide into 10 portions (about ¼ cup each) and shape into patties the same size as the buns.
3. Heat a barbecue to medium-low. Split the buns in half and grill, cut side down, on the barbecue for 30 seconds or until lightly golden. Remove and set aside.
4. Grease the burger patties with olive oil. Cook on the preheated grill plate for 6-7 minutes each side or until cooked through. Put a quarter piece of cheese on top of each patty. Cover the barbecue with the lid until the cheese is just melted.
5. Spread 2 teaspoons of aioli on each bun base and top with a piece of lettuce and a burger patty. Top with burger relish, a bread and butter cucumber and drained pickled onions. Finish with a bun top and skewer to secure. Serve.