Preheat oven to 425°.
To prepare eggplant, place eggplant on several layers of paper towels; sprinkle evenly with 1 teaspoon salt. Cover with additional paper towels; let stand 10 minutes, pressing down occasionally. Lightly coat each slice with cooking spray; sprinkle with 1/4 teaspoon pepper. Arrange eggplant in a single layer on 2 baking sheets. Bake at 425° for 8 minutes. Turn eggplant slices over. Rotate baking sheets; bake an additional 8 minutes.
To prepare meat mixture, heat oil in a large nonstick skillet over medium-high heat. Add onion, 4 garlic cloves, and chicken; sauté 6 minutes or until chicken is done. Stir in bulgur, mint, 1/4 teaspoon pepper, 1/8 teaspoon salt, allspice, and tomatoes; bring to a boil. Cover, reduce heat, and simmer 20 minutes. Remove from heat; cool completely.
To prepare topping, melt butter in a medium saucepan over medium heat. Add flour, stirring with a whisk until well blended. Gradually add milk, stirring with a whisk until blended. Add 2 garlic cloves; bring to a boil. Reduce heat to low; cook 2 minutes or until thickened, stirring constantly with a whisk. Pour milk mixture into a food processor; add feta and nutmeg. Process until smooth; stir in yogurt.
Coat 2 (8-inch) square baking dishes with cooking spray. Divide half of eggplant slices between each dish; top each with 1 cup meat mixture. Repeat procedure with remaining eggplant and the remaining 2 cups meat mixture. Pour 1 1/4 cups topping mixture over each. Bake at 425° for 35 minutes or until top is bubbling.