Stir in spinach; cook until wilted and all of its moisture has evaporated. Remove the pan from the heat and stir in the cooked chicken. Set it aside.
In a small bowl make a slurry by whisking together 1/2 cup chicken stock with flour. It should be thick milky consistency. Set it aside. In a small saucepan, combine the remaining 1 1/2 cups chicken broth, milk, nutmeg, and 1 teaspoon of salt. Bring to a slow simmer over medium heat, stirring occassionally. Once the mixture starts to bubble up around the edges, add the slurry while whisking nonstop. Simmer until thickened, about 5-8 minute, whisking occassionally. Stir in Parmesan cheese and then remove from heat.
Pour 1/2 cup sauce into bottom of 10X10 square baking dish, top with 2 noodles, 1 cup chicken mixture, 1 cup sauce, and 1/4 cup mozzarella, making sure noodles are covered with sauce. You can even press them down lightly. Repeat 3 more layers with noodles, chicken, sauce, and cheese. Last layer will have slightly more sauce and remaining cheese on top.
Cover baking dish with aluminum foil and bake for 25 minutes. Uncover and bake for 15 minutes longer. If desired, broil for 2-3 minutes for golden brown top. Let stand 15-20 minutes before cutting and serving.