Cook lasagna noodles, omitting salt and fat. Drain; set aside.
Preheat oven to 375°.
Heat oil in a Dutch oven coated with cooking spray over medium heat until hot. Add broccoli and next 4 ingredients (broccoli through garlic), and sauté 7 minutes. Set aside.
Place flour in a medium saucepan. Gradually add milk, stirring with a whisk until blended. Bring to a boil over medium heat; cook 5 minutes or until thick, stirring constantly. Add 1/4 cup Parmesan cheese, salt, and pepper; cook 1 minute, stirring constantly. Remove from heat; stir in spinach. Reserve 1/2 cup spinach mixture for top layer of casserole, and set aside.
Combine cottage cheese, mozzarella, and Swiss cheese; stir well. Spread 1/2 cup spinach mixture in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange 4 lasagna noodles over spinach mixture in dish; top with half of cottage cheese mixture, half of broccoli mixture, and half of remaining spinach mixture. Repeat layers, ending with noodles. Spread reserved 1/2 cup spinach mixture over noodles; sprinkle with 1/4 cup Parmesan cheese. Cover and bake at 375° for 35 minutes. Let stand 10 minutes before serving. Sprinkle with pepper, if desired.