Salt eggplant and let drain on kitchen towels for 30 minutes; press out excess liquid.
Preheat oven to 375°F.
Set up breading station: Season flour with salt and pepper in shallow dish. Whisk up eggs in a shallow dish and season with salt and pepper. Combine panko, fine crumbs, salt, pepper, 1 cup of the grated Parmigiano-Reggiano cheese and parsley in another dish. If not using cooking spray, moisten the bread with olive oil. Coat eggplant in flour, egg then breadcrumb mixture. Arrange on 2 large baking sheets, spray liberally with cooking spray (if using) on both sides. Bake eggplant 10-12 minutes then turn and bake 10-12 minutes more until crispy and brown on both sides.
For the creamed spinach, heat a medium skillet over medium heat with oil, 2 turns of the pan. Add shallots and garlic, and soften 3-5 minutes. Add Boursin or cream cheese and melt; add half-and-half to thin a bit. Season with nutmeg, salt and pepper. Add spinach and heat through; fold in grated cheese.
For the mushrooms, heat a large skillet over medium-high heat with olive oil, two turns of the pan. Add mushrooms and brown; season with salt and pepper. Deglaze the mushrooms with brandy or dry sherry.
For the béchamel, melt butter in a saucepot over medium heat. Stir in flour and cook a minute or two. Pour in warm milk and thicken, stirring constantly. Season with salt, pepper and nutmeg to taste.
Switch on broiler and place a rack in the center of oven.
Make stacks of a slice of crispy eggplant, some spinach, mushrooms, another slice of eggplant, a dollop or two of sauce and a sprinkle each of Fontina or mozzarella and some Parmigiano-Reggiano. Arrange stacks in large shallow casserole or lasagna pan and carefully broil until tops are lightly browned and bubbly.