01 - Preheat the oven to 375°F. Grease a 9x13-inch baking dish and set aside.
02 - Cook the lasagna noodles according to package instructions; drain and lay flat on a clean surface to prevent sticking. Skip this step if using no-boil noodles.
03 - Heat olive oil in a large skillet over medium heat. Sauté the finely chopped onion until softened, about 3 minutes. Add the minced garlic and cook for 1 additional minute until fragrant.
04 - Stir in the spinach and cook until wilted. Transfer the mixture to a mixing bowl and combine with the shredded chicken. Season with salt, pepper, and half of the dried Italian herbs. Set aside.
05 - In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 2 minutes to form a roux. Slowly pour in the whole milk and heavy cream, whisking constantly until the sauce thickens, 5 to 7 minutes. Stir in the nutmeg, remaining Italian herbs, and a pinch of salt and pepper. Remove from heat and fold in the ricotta and half of the Parmesan cheese until smooth.
06 - Spread a thin layer of the white sauce across the bottom of the prepared baking dish. Layer with 3 noodles, half of the chicken-spinach mixture, one-third of the mozzarella, and one-third of the remaining sauce. Repeat the layers once more, then finish with a top layer of noodles, the remaining sauce, and all leftover mozzarella and Parmesan cheeses.
07 - Cover the dish tightly with aluminum foil and bake for 35 minutes. Remove the foil and continue baking for 15 to 20 minutes until the top is golden and bubbling. Let the lasagna rest for 10 to 15 minutes before slicing and serving.