Place eggplant in a large bowl; sprinkle with 1 teaspoon salt. Let stand 30 minutes. Rinse and drain; pat dry with paper towels.
Spoon yogurt onto several layers of heavy-duty paper towels; spread to 1/2-inch thickness. Cover with additional paper towels; let stand 10 minutes. Scrape into a bowl using a rubber spatula; cover and refrigerate.
Place half the eggplant slices on a broiler pan coated with cooking spray; broil 6 minutes on each side or until lightly browned. Repeat procedure with the remaining eggplant.
Cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a broiler pan; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes; peel.
Place the potato slices on a broiler pan coated with cooking spray; broil 7 minutes per side or until golden on both sides.
Arrange potato slices in the bottom of a 13 x 9-inch baking dish coated with cooking spray. Top with eggplant slices. Arrange bell pepper halves over eggplant.
Heat a large nonstick skillet over medium-high heat. Add lamb; sauté 5 minutes or until browned, stirring to crumble. Drain well; return to pan. Add onion; sauté 5 minutes. Stir in tomato and next 5 ingredients (tomato through cinnamon stick); bring to a boil. Reduce heat, and simmer 8 minutes. Sprinkle with 1/2 teaspoon salt and 1/8 teaspoon black pepper; discard cinnamon stick. Spoon over bell pepper halves.
Preheat oven to 400°.
Lightly spoon the flour into a dry measuring cup, and level with a knife. Combine the olive oil and flour in a large saucepan over medium heat, stirring with a whisk. Cook for 3 minutes, stirring frequently. Combine the drained yogurt and milk. Add the yogurt mixture to flour mixture, stirring continuously; cook until thick (do not boil). Remove from heat; stir in 3/4 cup cheese, 1/4 teaspoon salt, 1/8 teaspoon black pepper, dash of nutmeg, and egg yolks.
Spoon the sauce over the lamb mixture; spreading carefully, run a knife around outside edge to allow sauce to run into dish (dish will be very full). Place on a foil-lined baking sheet. Bake at 400° for 45 minutes or until golden brown and bubbly. Let stand 20 minutes.