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1
Place the eggplant slices in a large bowl and cover with water.
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2
Add 1/2 cup of salt and agitate gently to combine.
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3
Let stand for 20 minutes, then drain and pat dry with paper towels.
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4
While the eggplant is soaking, heat 1/2 cup of the olive oil in a large skillet and, working in batches, add the potato slices and cook until lightly golden on both sides, 3 to 4 minutes.
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5
Transfer to a paper-lined plate to drain and repeat with any remaining potato slices.
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6
Season lightly with salt.
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7
Place 1 cup of the flour in a bowl and dredge the eggplant slices in the flour.
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8
Shake to remove any excess flour.
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9
Add 1/4 cup of the remaining oil to the skillet and, working in batches, fry the eggplant slices until golden on both sides, 2 to 3 minutes per side.
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10
Add more oil to the skillet as needed in 1/4 cup increments.
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11
Repeat until all eggplant has been cooked.
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12
Transfer to a paper-lined plate to drain.
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13
Heat 2 tablespoons of the butter in a large skillet and, when melted, add the onions.
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14
Cook until tender, about 4 minutes.
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15
Add the ground meats, garlic, and oregano and cook, stirring to break up any lumps, until meat is browned, 4 to 6 minutes.
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16
Add the red wine and cook until evaporated.
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17
Add the tomato paste and cook, stirring, for 1 minute.
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18
Add the crushed tomatoes, water and parsley and cook, stirring occasionally, until almost all liquid is evaporated, 5 to 10 minutes.
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19
Season, to taste, with salt and pepper and set aside.
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20
In a medium saucepan melt the remaining 3 tablespoons of butter and, when hot, whisk in the flour and cook, stirring, for 2 to 3 minutes.
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21
Gradually whisk in the milk, stirring until smooth and thick.
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22
Season with salt, to taste, and whisk in the egg and egg yolk.
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23
Stir in 1/2 cup of the cheese and set aside, covered, while you assemble the casserole.
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24
Preheat the oven to 350 degrees F. Lightly grease a 9 by 13-inch casserole dish and place the sliced potatoes in the bottom of the dish in an even layer.
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25
Top with half of the eggplant slices and half of the meat sauce.
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26
Spoon 3/4 cup of the bechamel sauce evenly over the meat sauce and sprinkle with 1/2 cup of the cheese.
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27
Top with the remaining eggplant slices, pressing down on the layers gently with your hands to compress.
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28
Top with the remaining meat sauce and then spread the remaining bechamel sauce evenly over the top.
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29
Sprinkle with the remaining cheese.
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30
Bake, uncovered, until golden brown on the top and heated throughout, 50 minutes to 1 hour.
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31
Let stand for at least 40 minutes before cutting into squares and serving.
