Rinse the split peas, then leave them to soak in cold water for 1 hour. Drain, then tip into a heavy-based saucepan with the turmeric, garlic and salt. Pour over the stock and bring to the boil, then reduce the heat, cover with a lid and simmer gently for 1 hour until almost all the liquid has been absorbed.
Meanwhile, prepare the spicy aubergine. Cut each aubergine widthways into thirds, then slice each piece into wedges. ?Heat a splash of oil in a deep frying pan and fry, in batches, over a medium heat for about 10 minutes until golden, transferring to a plate lined with kitchen paper as you go. Return all the aubergine to the pan, then increase the heat, add the garlic and fry for 2 minutes. Sprinkle in the cumin seeds and fry for a further minute, then add the tomato purée and harissa to taste and fry for 2 minutes. Pour over the stock – it will bubble up viciously at this point, so stand back to avoid getting splattered – and cook for 3–4 minutes until the liquid has mostly been absorbed. Remove from the heat and stir in the vinegar.
Thinly slice the fennel on a mandolin or using a very sharp knife, then toss with the salt in a bowl. Massage the fennel for a minute or so until it begins to soften slightly, then squeeze over the lemon juice.
Pour the cooked split peas into a liquidiser, add the extra virgin olive oil and blend to a smooth purée – add a little water if it needs some encouragement. Pour into a clean pan and set aside.
To serve, gently reheat the split pea purée, divide between warmed serving bowls, spoon over the spicy aubergine and top with the fennel.