Preheat oven to 450°F. Place eggplant halves, cut-side down, in a roasting pan. Add water to a depth of 1/2 inch. Bake until tender, 20 to 25 minutes; set aside. Reduce oven temperature to 400°F.
While the eggplant is roasting, heat a large nonstick skillet over medium-high heat. Add ground lamb and sauté, breaking up the meat with a wooden spoon, until browned, 3 to 5 minutes. Transfer to a colander and drain off fat. Set aside.
Heat oil in a Dutch oven over medium heat. Add onions and cook until golden, about 5 minutes. Add red peppers and garlic and cook for 2 minutes longer. Stir in tomatoes and their juice, oregano, thyme, cinnamon and cloves. Simmer, breaking up the tomatoes with a wooden spoon, until the mixture has thickened slightly, 3 to 5 minutes.
Scoop out eggplant flesh and chop coarsely. Stir rice, broth, chopped eggplant and the reserved lamb into the tomato mixture; bring to a simmer. Cover the pan and place it in the oven. Bake for 30 to 35 minutes, or until the rice is tender and the liquid has been absorbed. Season with salt and pepper. Dot with feta and serve.