Prick the aubergines, then carefully blacken them over a direct flame on the hob (or under the grill), turning with tongs until soft inside. Meanwhile, toast the sesame seeds in a large non-stick frying pan on a high heat until golden, tossing regularly. Put two-thirds of the toasted seeds into a blender, saving the rest for later. Drain the chickpeas (reserving the juice) and add two-thirds to the blender with the juice of 1 lemon and 2 tablespoons of extra virgin olive oil. Blitz until super-smooth, loosening with splashes of chickpea juice, if needed, then season to perfection and divide between plates.
Halve the radishes, toss with the remaining lemon juice and season with sea salt to quickly pickle. Once cool enough to handle, carefully remove the aubergine skin, then halve lengthways leaving them intact at the stalk, and season with salt and black pepper. Return the frying pan to a medium heat with a drizzle of olive oil, and scatter in the remaining chickpeas. Push the chickpeas to one side, then add the aubergines and cook for 5 minutes, or until the chickpeas are golden and crispy and the aubergine is starting to caramelize, turning as needed. Divide between plates, scatter over the reserved toasted sesame seeds and radishes, and finish with a drizzle of extra virgin olive oil, if you like.