Step 1
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil; place eggplant halves on top.
Step 2
Broil eggplant checking fairly often and rotating the baking sheet as needed until the skin blackens and starts to char in places about 15 minutes. Cool until easily handled about 5 minutes. Peel off skin and coarsely chop flesh.
Step 3
Heat olive oil in a large skillet over medium heat. Add onions; cook and stir over medium heat until onion is translucent about 5 minutes. Add lamb and cook breaking it up into small pieces until no pink remains about 5 minutes. Drain grease from the skillet.
Step 4
Stir minced garlic salt cumin oregano pepper and cinnamon into the skillet; cook for 1 minute. Stir in chopped eggplant diced tomatoes and crushed tomatoes. Bring sauce to a simmer and cook until thickened about 20 minutes. Remove from heat and stir in chopped mint.
Step 5
Melt butter in a saucepan over medium heat. Stir in flour and cook stirring constantly for 2 minutes. Pour in milk and whisk until smooth. Add crushed garlic clove increase heat to high and bring milk to a boil. Reduce heat and simmer stirring frequently until slightly thickened about 5 minutes more. Remove from heat; discard garlic clove.
Step 6
Whisk eggs in a large heatproof bowl. Pour hot milk mixture in a steady stream into beaten eggs whisking constantly. Stir in feta cheese salt pepper and nutmeg.
Step 7
Preheat oven to 425 degrees F (220 degrees C). Spray a 9x13-inch baking dish with cooking spray.
Step 8
Bring a large pot of salted water to boil. Add pasta and cook stirring occasionally until tender yet firm to the bite about 12 minutes. Drain.
Step 9
Divide pasta between the white sauce and the lamb sauce and mix to combine. Pour the pasta with lamb sauce into the prepared baking dish; spread the pasta with white sauce on top.
Step 9
Bake in the preheated oven until top is golden and pastitsio is bubbling about 30 minutes. Let cool for 5 minutes before serving.