Preheat oven to 350 degrees F (175 degrees C). Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in boiling water for 8 to 10 minutes. Drain, and rinse with cold water.
Melt the butter in a large saucepan over medium heat. Cook the onion and garlic in the butter until tender, stirring frequently. Stir in the flour and salt, and simmer until bubbly. Mix in the broth and milk, and boil, stirring constantly, for 1 minute. Stir in 2 cups mozzarella cheese and 1/4 cup Parmesan cheese. Season with the basil, oregano, and ground black pepper. Remove from heat, and set aside.
Spread 1/3 of the sauce mixture in the bottom of a 9×13 inch baking dish. Layer with 1/3 of the noodles, the ricotta, and the chicken. Arrange 1/3 of the noodles over the chicken, and layer with 1/3 of the sauce mixture, spinach, and the remaining 2 cups mozzarella cheese and 1/2 cup Parmesan cheese. Arrange remaining noodles over cheese, and spread remaining sauce evenly over noodles. Sprinkle with parsley and 1/4 cup Parmesan cheese.
Bake 35 to 40 minutes in the preheated oven.
Aluminum foil can be used to keep food moist, cook it evenly, and make clean-up easier.