Preheat the oven to 425°F on the roast setting. For Miele clients, use Convection Roast at 425°F
Arrange the eggplant halves cut-side up on large baking sheets. Drizzle with olive oil and season lightly with salt and pepper. Roast for 40–50 minutes, or until the eggplants are completely tender and easily pierced with a fork.
Allow the eggplants to cool slightly. Scoop the flesh into a bowl, incorporating some of the softened skin for added flavor and texture. Transfer to a food processor or blender and pulse until mostly smooth with a few small chunks remaining.
Meanwhile, heat 3 tablespoons of olive oil in a large skillet over medium-low heat. Add the sliced onions and a pinch of salt and pepper. Cook slowly, stirring occasionally, for about 25 minutes, until deeply golden and caramelized.
Remove about one-third of the onions and reserve for garnish.
Increase the heat to medium. Add the garlic, dried mint, and turmeric to the skillet. Cook for 1–2 minutes, stirring constantly, until fragrant. Reserve a small spoonful of this mixture for garnish.
Add the blended eggplant mixture to the skillet and stir to combine. Bring to a gentle simmer and cook for 5–10 minutes to allow the flavors to meld.
Remove from the heat. Stir in ½ cup of the kashk and season with the remaining salt and pepper to taste.
Transfer the Kashk-e-Bademjan to a serving dish. Using a spoon, create decorative circular layers of the reserved caramelized onions, garlic-mint mixture, and remaining kashk over the surface. Top with chopped walnuts (optional) in the center if desired
Serve warm with fresh lavash or other Persian flatbread.