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**Eggplant Puree (Hünkar Beğendi):**
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1. Preheat oven to 400°F (200°C). Pierce eggplants several times with a fork. Rub with olive oil and place on a baking sheet. Roast for 45-60 minutes, or until the skin is blackened and the eggplant is very soft. Alternatively, you can grill or smoke the eggplants over an open flame until blackened. This imparts a more intense smoky flavor.
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2. Let the eggplants cool slightly. Then, peel off the skin and discard. Chop the eggplant flesh roughly.
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3. In a saucepan, melt butter over medium heat. Add flour and cook for 1-2 minutes, stirring constantly, until golden brown.
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4. Gradually whisk in milk until smooth and there are no lumps.
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5. Add the chopped eggplant, salt, and pepper. Cook for 5-7 minutes, stirring constantly, until the mixture thickens and becomes creamy.
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6. Stir in the grated kashar cheese (or mozzarella) until melted and combined. Set aside and keep warm.
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**Lamb Stew:**
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7. Heat olive oil in a large pot or Dutch oven over medium-high heat. Season the lamb with salt and pepper.
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8. Brown the lamb in batches, ensuring not to overcrowd the pot. Remove the lamb and set aside.
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9. Add onion, green bell pepper, and red bell pepper to the pot and cook until softened, about 5-7 minutes.
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10. Add garlic and tomato paste. Cook for 1 minute more, stirring constantly.
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11. Deglaze the pot with red wine (if using), scraping up any browned bits from the bottom.
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12. Return the lamb to the pot. Add diced tomatoes, oregano, thyme, bay leaf, and beef broth (or lamb broth).
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13. Bring to a boil, then reduce heat to low, cover, and simmer for 2-2.5 hours, or until the lamb is very tender.
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14. Remove the bay leaf. Season with salt and pepper to taste.
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**To Serve:**
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15. Spoon a generous amount of the smoked eggplant puree onto each plate.
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16. Top with the rich lamb stew.
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17. Garnish with fresh parsley, if desired. Serve immediately.