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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.
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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.
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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.
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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.
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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.
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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.
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7
Preheat oven to 425 degrees F (220 degrees C). Spray a 9x13-inch baking dish with cooking spray.
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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.
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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.
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10
Bake in the preheated oven until top is golden and pastitsio is bubbling, about 30 minutes. Let cool for 5 minutes before serving.
