In a medium saucepan over medium heat, melt butter. Cook onion and garlic in butter until tender. Stir in flour, pepper, 1/2 teaspoon salt and nutmeg. Stirring continuously, pour in milk, a little at a time, allowing mixture to thicken. Bring to a boil for 1 minute, then remove from heat and stir in parsley. Set aside.
In a medium bowl, combine ricotta, broccoli, Parmesan, 1 cup of mozzarella and remaining 1/2 teaspoon salt. Stir until well blended.
In a 7x11 inch baking dish layer: 1/4 cup white sauce; 3 noodles; one-third of remaining white sauce; half the broccoli mixture; 3 more noodles; half remaining white sauce; remaining broccoli mixture; 3 noodles; remaining white sauce. Sprinkle with remaining mozzarella. Cover with foil coated with cooking spray.
Bake in preheated oven 30 minutes. Let stand 10 minutes before serving.