Preheat the oven to 200°C. Pierce each aubergine several times with a fork and place on a baking tray. Roast until softened and collapsed which usually takes 35 to 40 minutes. Allow them to cool slightly before peeling the skins. Move to the next step once peeled.
Transfer the warm peeled aubergine into a bowl and mash gently with a fork. Aim for a coarse texture rather than a smooth puree as this gives the dish more character. Set aside while preparing the aromatics.
Warm two tablespoons of olive oil in a large pan. Add the sliced onions and cook slowly over medium heat until golden and softened. A patient approach here helps build the caramelised depth needed for an authentic flavour. Leave a small portion aside for garnish then continue.
Stir the minced garlic and turmeric into the pan with the remaining onions. Cook until fragrant which should take about one minute. Keep the heat moderate to avoid burning the garlic. Transition to the next step once the mixture is aromatic.
Add the mashed aubergine to the pan and fold gently to combine. Season with salt and black pepper. Cook for several minutes to allow the flavours to seep into the aubergine. Continue once well blended.
Pour in half of the diluted kashk and stir thoroughly. Allow the mixture to simmer on low heat for 5 to 8 minutes. If it thickens too quickly add a splash of water to loosen it. Move forward once the texture is creamy.
In a small pan heat the remaining olive oil and add the dried mint. Let it sizzle briefly until the aroma lifts but remove promptly to prevent bitterness. This mint oil will be used for flavour and garnish. Proceed to the next step.
Taste the dish and adjust the salt and pepper. Add more kashk if a stronger tang is desired or reduce the heat and simmer further if you prefer a thicker consistency. Transition to the final assembly.
Spoon the Kashk e Bademjan into a shallow serving dish. Drizzle the remaining kashk over the top and swirl gently. Add the mint oil followed by the reserved fried onions and walnuts if using.
Serve warm alongside fresh flatbread or lavash. Garnish lightly to highlight the pale aubergine base and aromatic toppings. This dish pairs beautifully with herbs and simple salads for a balanced table.