We based the recipe for this Greek dish on one in the Moosewood Cookbook by Mollie Katzen (Ten Speed Press, 1977).
1 tbsp. olive oil
3 medium eggplants (about 3 lbs.),
cut lengthwise into 1⁄4"-thick slices
Kosher salt and freshly ground black pepper, to taste
1 cup (2 sticks) plus 3 tbsp. butter
2 lbs. button mushrooms, thickly sliced
2 cloves garlic, finely chopped
1⁄4 cup dry red wine
1⁄4 cup chopped flat-leaf parsley leaves
2 tbsp. finely chopped basil leaves
1 tbsp. finely chopped oregano leaves
1 tsp. ground cinnamon
1 6-oz. can tomato paste
1 1⁄4 cups grated parmigiano-reggiano
3⁄4 cup bread crumbs
4 beaten eggs plus 4 egg yolks
1⁄2 cup flour
2 1⁄2 cups milk
1. Heat oven to 350°. Grease 2 baking sheets with oil; arrange eggplant on them in a single layer; season with salt and pepper. Bake, turning once, until soft, about 20 minutes; set aside.
2. Heat 10 tbsp. butter in a large pot over medium-high heat. Add mushrooms, garlic, onions, and salt and pepper. Cook until mixture is mostly dry, 18–20 minutes. Add wine, parsley, basil, oregano, cinnamon, tomato paste, and salt and pepper. Reduce heat to medium-low; cook until liquid is absorbed, 4-5 minutes. Remove from heat and stir in 1⁄2 cup parmigiano, 1⁄2 cup bread crumbs, and whole eggs. Set aside.
3. Melt 8 tbsp. butter in a saucepan over medium-low heat. Whisk in flour; cook, stirring constantly, for 2 minutes. Whisk in milk and cook, whisking, until thickened, 1–2 minutes. Remove sauce from heat; stir in egg yolks and salt and pepper; set sauce aside.
4. Grease a 9" × 13" casserole dish with remaining butter. Cover bottom with half the eggplant, then half the mushroom mixture. Repeat. Top with reserved sauce; sprinkle with remaining bread crumbs and parmigiano. Cover with foil; bake until hot, 35–40 minutes. Uncover; bake 15 minutes more. Let rest for 15 minutes before serving.