To make the hummus, crush the garlic and the sesame seeds together in a pestle and mortar until they form a paste.
Place the paste in a small food processor and add the chickpeas, olive oil, seasoning and lemon juice. Pulse and add just enough water to make a smooth paste.
Spoon the chickpea mixture into a serving bowl, drizzle with olive oil and a sprinkle a pinch of cayenne over the top.
To make the aubergine crisps, pour the vegetable oil and olive oil into a deep, heavy-based saucepan and heat until a small cube of bread sizzles and turns golden when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Add the aubergine slices to the hot oil and fry gently for eight minutes, or until crisp and golden-brown. Carefully remove with a slotted spoon and drain on kitchen paper.
To serve, scatter the aubergine crisps with sea salt and place around the bowl of hummus.