Cut stems from silver beet; chop finely, then tear leaves.
Heat oil in a 3 litre (12-cup), 30cm (top measurement) ovenproof frying pan or round cast iron dish over high heat. Add silver beet stems, eggplant, onion and garlic; cook, stirring occasionally, for 8 minutes or until eggplant is golden and onion is soft. Add harissa; cook for 1 minute. Add tomatoes, stock, silver beet leaves and basil. Reduce heat to low; cook for 5 minutes. Season to taste. Transfer to a bowl.
Meanwhile, process pine nuts and parmesan until chopped finely. Transfer to a small bowl.
Make cheesy yoghurt topping. Whisk ingredients in a bowl until smooth and combined.
Wipe frying pan clean; oil lightly. Place two lasagne sheets over base; top with half the eggplant mixture. Top with another two lasagne sheets, then remaining eggplant mixture, spreading out evenly. Top with another two lasagne sheets, pressing down gently onto eggplant mixture. Spread with cheesy yoghurt topping; cover pan with foil.
Bake lasagne for 25 minutes. Remove foil; sprinkle with pine nut mixture. Bake, uncovered, for a further 15 minutes or until lasagne is bubbling and pine nut mixture is golden.
Drizzle lasagne with extra oil and sprinkle with small basil leaves, if you like. Serve.