Sprinkle eggplant slices with a little salt, set aside.
In skillet cook meat and onion until meat is brown; drain off excess fat. Stir in wine, water, parsley, tomato paste and 1 teaspoon of salt, and dash of pepper. Simmer until liquid is nearly evaporated, about 4 minutes. Cool slightly.
Stir half of the breadcrumbs, half of the cheese, the 2 eggs, and cinnamon until meat mixture, set aside.
In saucepan melt butter; stir in flour, the 1/2 teaspoon salt, nutmeg, and the dash of pepper. Add milk all at once; cook and stir until thickened and bubbly. Stir half of the sauce into the one beaten egg to temper. Return back to saucepan. Cook and stir over low heat for 2 minutes, set aside.
Brown eggplant sauces in a little hot oil. Sprinkle bottom of a 12x7 1/2x2 inch baking dish with remaining bread crumbs. Cover with half of the eggplant.
Spoon meat mixture over the eggplant layer. Arrange remaining eggplant atop; pour milk-egg sauce over all. Sprinkle with remaining 1/4 cup cheese. Bake, uncovered, at 350 till set, about 45 minutes.