||Heat 1-½ cups milk and butter in a small pan until bubbles begin to appear around the rim. Remove from the heat.
||In a heavy 2 - 3 quart saucepan, beat the eggs, the remaining ½ cup of milk, the flour and salt together until smooth. Cook over moderate heat, stirring constantly, adding the milk and melted butter mixture in a thin stream. Cook until the sauce comes to a boil and becomes quite thick. Set aside.
||Preheat the oven to 325°.
||Assemble the moussaka; spread half the eggplant slices in overlapping rows in the bottom of a 14"x9"x3" baking dish.
||Sprinkle with 2 tablespoons of the parmesan cheese and pour in the lamb mixture, spreading it evenly over the eggplant. Arrange the rest of the eggplant on top, then 2 more tablespoons of the cheese.
||Pour the sauce evenly over the eggplant; sprinkle the remaining cheese on top.
||Bake for 30 minutes, then increase heat to 400° and bake 15 minutes longer.
||Let rest 5 to 10 minutes before serving.