Preheat oven to 375F.
Heat a large nonstick skillet over-medium high heat; add oil, onions, garlic, mushrooms, basil, oregano, red pepper flakes, and ¼ tsp salt. Sauté about 3-4 minutes, or until mushrooms softened and their liquid has mostly evaporated.
Add fresh spinach and cook until wilted, about 10-15 seconds. Remove the pan from heat and stir in chicken.
In a small bowl, whisk ½ cup chicken broth with flour, until a thick consistency is formed; set aside. Combine remaining 1 ½ cups broth, milk, nutmeg, and 1 tsp salt in a medium saucepan and simmer over medium heat, stirring occasionally. Once bubbly, add the slurry and whisk continuously.. Simmer until thickened (about 6 minutes) and stir in parmesan. Remove from heat.
Pour ½ cup sauce into the bottom of a large cast iron skillet. Top with ⅓ of the noodles, 1 cup chicken mixture, 1 cup sauce, and ¼ cup mozzarella. Repeat layers three times, finishing with sauce and cheese.
Cover the baking dish with foil and bake for 20-25 minutes, or until bubbly.
