01 - Preheat the oven to 375°F. Lightly grease a 9x13 inch baking dish with butter or nonstick spray.
02 - Cook the lasagna noodles according to package directions until al dente. Drain thoroughly and lay them flat on a clean surface to prevent sticking.
03 - Heat olive oil in a large skillet over medium heat. Add the onion and mushrooms, sautéing for 4 minutes until softened. Stir in the garlic and chopped spinach, cooking for an additional 2 minutes until the spinach is fully wilted.
04 - Add the shredded chicken to the skillet with the vegetables. Season with dried basil, dried thyme, black pepper, and salt. Toss to combine evenly, then remove from heat and set aside.
05 - In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute to form a roux. Gradually pour in the whole milk while whisking constantly to prevent lumps. Bring the mixture to a gentle simmer and cook for 5 to 6 minutes, stirring frequently, until the sauce thickens enough to coat the back of a spoon. Stir in 1/2 cup of the Parmesan cheese and the nutmeg, then remove from heat.
06 - Spread a thin layer of the white sauce across the bottom of the prepared baking dish. Arrange 3 noodles over the sauce. Layer half of the chicken and vegetable mixture over the noodles, followed by one-third of the ricotta, one-third of the mozzarella, and one-quarter of the remaining sauce. Repeat with another layer of 3 noodles, the remaining chicken mixture, another third of the ricotta, another third of the mozzarella, and another quarter of the sauce. Finish with a final layer of the remaining noodles, the rest of the sauce, the remaining ricotta and mozzarella, and top with the remaining Parmesan.
07 - Cover the baking dish tightly with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for 15 minutes, or until the top is golden brown and the edges are bubbling.
08 - Remove the lasagna from the oven and let it rest for 10 to 15 minutes to allow the layers to set before slicing into portions and serving.