Preheat oven to 425.
Prepare eggplant: Peel eggplants and slice into 1/2" slices. Lay slices on several layers of paper towels; sprinkle evenly with 1 teaspoons salt. Cover with additional paper towels and let stand for about 10 minutes, pressing down occasionally. Lightly coat each slice with cooking spray and sprinkle with 1/4 teaspoons black pepper. Arrange slices in a single layer on 2 baking sheets. Bake for 8 minutes at 425; take out and turn slices over, then bake for another 8 minutes. Remove from oven and set aside.
Prepare meat mixture: Heat oil in large nonstick skillet. Add onion, garlic and ground turkey; saute 6-8 minutes, or until turkey is done. Stir in bulgur, mint, pepper, salt, allspice, and tomatoes. Bring to a boil, then cover and reduce heat. Simmer 20 minutes. Remove from heat and cool completely.
Prepare topping: Melt butter in a saucepan over medium heat. Add flour, stirring with a whisk until well blended. Slowly add milk, stirring with whisk until blended. Add four minced garlic cloves. Bring to a boil, then reduce heat to low, cooking 2 minutes or until thickened, stirring constantly with whisk. Pour milk mixture into a food processor. Add feta and nutmeg, process until smooth, then stir in yogurt.
Assemble: Coat a 13x9 pan with cooking spray. Place half the eggplant slices in bottom of pan, then cover with half the meat sauce. Layer remaining eggplant slices, top with remaining meat sauce. Spoon topping mixture evenly over top. Bake at 425 for 35 minutes.