Set your oven to preheat at 375°F while you prep the filling.

In a large skillet over medium-high heat, warm the olive oil, then toss in the onion, garlic, mushrooms, basil, oregano, red pepper flakes, and a pinch of the salt. Cook for roughly 5 minutes, stirring now and then, until the mushrooms release their moisture and it fully cooks away.

Add the spinach directly into the pan and continue cooking until it wilts completely and no excess liquid remains. Take the pan off the heat, fold in the shredded chicken, and set the mixture aside.

Whisk a portion of the chicken broth with the flour in a small bowl until you get a smooth, thick paste — this is your thickening slurry. In a separate saucepan, warm the rest of the broth together with the milk, nutmeg, and remaining salt over medium heat until small bubbles form at the edges. Pour in the slurry while whisking continuously, then let it simmer for 5-7 minutes until it thickens into a sauce. Stir in the Parmesan until melted, then remove from heat.

Spread a thin layer of sauce across the bottom of a greased baking dish. Layer noodles on top, followed by the chicken-mushroom-spinach mixture, more sauce, and a sprinkle of mozzarella. Continue layering until you've used everything, finishing with a generous topping of sauce and cheese.

Cover the dish with foil and bake for about 25 minutes, then remove the foil and bake uncovered for another 15 minutes until bubbly. For a golden top, broil briefly for 2-3 minutes. Let it rest for 15 minutes before slicing so it holds together.