Rinse the avocado, halve them and remove the stone. Peel the avocados and place the flesh in a blender with the lemon juice. Cut the chilli lengthwise, remove any seeds, and finely chop. Add cane sugar and salt.
Peel the carrots and grate in broad strips, for instance with a peeler. Combine the yoghurt, garlic, salt and pepper. Stir it into the carrots.
Divide the meat into 4 portions. Form into large flat patties. Brown them in butter and oil in a very hot frying pan for about 1 min. on each side. Season with salt and pepper. Continue cooking for an additional 2-3 min. on each side over a medium heat. The meat should be cooked to medium and the juices should run clear.
Toast the bread slices using a toaster or hot grill pan. Spread avocado cream on the bread slices. Assemble the beef sandwich by layering lettuce, hot beef patty, tomato slices and onion slices. Top with a slice of toasted bread – and press down slightly. Serve with the carrot salad and any remaining avocado cream.