Preheat the oven to 375�F. Coat a 9 x 13-inch casserole dish with cooking spray.
Cook the lasagna noodles according to package directions, then drain.
In a large cast-iron skillet, heat the oil over medium heat. Add the broccoli, carrots, onions, bell peppers, zucchini, and garlic. Saut� the vegetables for 7 minutes, then set aside.
Whisk flour and milk in a medium saucepan until blended. Bring the sauce to a boil over medium heat. Cook until thick (approximately 5 minutes), stirring constantly. Add 1/2 cup of Parmesan cheese, salt, and pepper to the saucepan. Cook for 1 minute, stirring constantly, then remove the saucepan from the heat. Add the spinach and stir. Set aside 1/2 cup of the spinach mixture. Mix the cottage and ricotta cheeses in a small bowl, stirring well.
Spread 1/2 cup of the spinach mixture onto the bottom of the casserole dish. Layer the noodles, ricotta mixture, vegetables, spinach mixture, and 2 cups of mozzarella cheese, ending with the noodles. Top with the reserved 1/2 cup of spinach mixture, 1/2 cup of mozzarella cheese, and 1/4 cup of Parmesan cheese.
Place casserole dish in oven and bake until lightly browned on top (approximately 35 minutes). Before serving, allow the lasagna to cool for approximately 10 minutes.
