Crispy Eggplant and Mushroom Lasagna

Name: Crispy Eggplant and Mushroom Lasagna
Ingredients: Canola oil; 1 cup all-purpose flour; 5 eggs, beaten; 1 1/2 cups panko bread crumbs; 1 tablespoon water; 1 eggplant, peeled, sliced into 1/8-inch discs; 8 portobello mushroom caps, gills removed; 1 tablespoon kosher salt, plus more for seasoning; 1 tablespoon cracked black pepper, plus more for seasoning; 1 cup white bean soup; 1 cup milk; 1 cup pesto, store-bought; 1 (14 1/2-ounce) can fire roasted tomatoes; 1 cup grated Parmesan; 2 (8-ounce) balls fresh mozzarella, thinly sliced