Mushroom Moussaka

Name: Mushroom Moussaka
Ingredients: 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 lb. 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