Bring a large saucepan of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
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 baking dish layer: 1/4 cup white sauce; 3 lasagne sheets; one-third of remaining white sauce; half the broccoli mixture; 3 more lasagne sheets; half remaining white sauce; remaining broccoli mixture; 3 lasagne sheets; 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.