Begin by charring the eggplants: Place whole eggplants directly over gas burner flames or under the broiler, turning frequently until the skin is completely blackened and the flesh is soft, about 15-20 minutes. Set aside to cool.

For the lamb stew: Heat olive oil in a large pot over medium-high heat. Cut the lamb into 1-inch cubes and season with salt and pepper. Brown the lamb in batches, about 4-5 minutes per batch. Remove and set aside.

In the same pot, add diced onions and cook until softened, about 5 minutes. Add minced garlic and bell peppers, cooking for another 3 minutes.

Return the lamb to the pot. Add diced tomatoes, tomato paste, paprika, cumin, black pepper, and bay leaves. Pour in enough water to cover the meat. Bring to a boil, then reduce heat to low.

Cover and simmer for 60-75 minutes until the lamb is fork-tender, stirring occasionally. If the sauce becomes too thick, add a splash of water.

While the lamb cooks, prepare the beğendi: Peel the cooled eggplants and mash the flesh in a bowl, discarding any seeds. Set aside.

In a large saucepan, melt butter over medium heat. Whisk in flour and cook for 2-3 minutes to create a roux, stirring constantly to prevent burning.

Gradually add milk while whisking continuously to prevent lumps. Cook until the mixture thickens, about 5-7 minutes.

Add the mashed eggplant to the white sauce, stirring well to combine. Cook for 5 minutes, stirring frequently.

Remove from heat and stir in grated cheese until melted and smooth. Season with salt and black pepper to taste.

To serve: Spread the creamy eggplant puree on a serving platter or individual plates. Ladle the lamb stew over the center, allowing the sauce to pool around the edges. Garnish with fresh parsley if desired.