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Scoop out the avocado flesh, cut into small cubes and put into a bowl. Using a serrated knife, cut the skin and pith away from the grapefruit, then segment over the bowl to catch all the juices. Cut the segments into cubes the same size as the avocado and add to the bowl.
Add the chilli and coriander and season the salsa with olive oil, salt, black pepper and lime juice to taste. The salsa can be made two hours in advance and kept covered in the fridge.
To serve, separate the larger chicory leaves, then finely chop the core and stir through the salsa. Spoon the salsa into each chicory leaf cup and place on a platter to serve.