Remove the stems from the aubergines and core with a small, serrated knife or corer. Remove the tops of the courgettes, peel, and core with a thin knife. Keep the pulp to prepare courgette cakes or courgette and sesame dip. Core and seed the Aleppo peppers and prepare the vine leaves by washing them well. Place them in a large plate, pour salted boiling water over them and let them cool. Drain and dry.
To make the stuffing: Soak the rice in boiled water for 10 minutes. Rinse in cold water and drain. Remove the skins of the tender chickpeas and half them. Heat the oil in a wide pan and fry the onions until translucent. Stir in the rice and add salt. Remove from heat and add the remaining ingredients. Mix well and taste to adjust the seasoning.
Fill the vegetables with the stuffing, remembering to leave space for the rice to swell. To stuff the vine leaves, lay them on a flat surface with the stem pointing towards you. Put a teaspoon of stuffing in the centre of the leaf, near the stem. Fold the sides and the end nearest to you over the stuffing and roll the leaf away from you to form a cylinder.
Cover the bottom of a heavy pan with slices of carrots, to avoid burning the stuffed vegetables. Place the stuffed vegetables on top, openings up, and fit the vine leaves down the side.
Combine all the ingredients for the broth except the oil, and pour the mixture into the pan. Drizzle the olive oil over the vegetables and place a small dish, inverted, on top. Cover the pot and boil on low heat for 45 minutes or until the rice is soft. Set aside for 10 minutes.
As the vegetables cool, they will absorb more of the cooking liquid. Arrange them on a large dish and serve with yoghurt