Trim the tops off the aubergines and chop the aubergines into dice around 1cm across. Warm a casserole for 2 mins over a medium-high heat, then add 2 tbsp olive oil and the aubergines. Season with a pinch of salt and pepper and fry for 5-8 mins, stirring often, till the aubergines are browned all over.
While the aubergines fry, peel and finely chop the onions. Trim the dry ends off the celery stick and finely slice it.
Scoop the aubergine out of the pan with a slotted spoon and pop in a plate. Turn the heat down to medium-low. Add another 1 tbsp olive oil to the pan and stir in the onion and celery. Season with a pinch of salt and pepper. Fry for 10 mins, stirring now and then, till the veg have picked up a little colour.
Trim the courgettes and dice them to match the aubergines. Halve the peppers, scoop out the white seeds and pith and chop them to match the courgettes. Roughly chop the tomatoes.
Stir the courgettes, peppers and tomatoes into the pan. Add the aubergines back in. Pop a lid on the pan and cook for 5 mins, stirring once or twice, to soften all the veg.
Scrub the potatoes and slice them into rounds around 1cm thick. Peel and crush the garlic. Drain the chickpeas and rinse them under cold water.
Stir the potatoes, garlic and chickpeas into the pan. Crumble in the stock cube. Pour in 800ml boiling water. Pop on the lid, turn the heat up and bring to the boil. When the stew is boiling, turn the heat down a little and simmer for 15 mins. The potatoes should be tender when pressed with a fork.
Taste the stew and add a pinch more salt and pepper if you think it needs it. Ladle the stew into bowls and tear over the basil leaves to garnish.