Preheat the oven to 350.
Bring a large pot of water to a boil. Add a few large pinches of salt to the water. Add the noodles and cook until just flexible and slightly softened--about 5 minutes. Remove to a cookie sheet sprayed with non stick spray. Set aside.
Heat a 9-inch skillet over medium-high heat. Add the olive oil and the onions. Cook 3 minutes then add the garlic stirring often.
Add the zucchini, carrots, mushrooms and spinach and cook until the vegetables release their water and it simmers away--about 6 minutes. Season with 1/4 of the salt and pepper. Set aside to cool slightly.
In a bowl, mix the cottage cheese, egg, Italian seasoning and oregano. Add the remaining salt and pepper to this mixture.
Place 1/3 of the pasta sauce in the bottom of a 9x13 or slightly smaller baking dish.
Working with one lasagna sheet at a time, spread a couple of tablespoons of the cheese/egg mixture over the length of the pasta. Sprinkle with a couple of tablespoons of the vegetables and add a tablespoon of mozzarella and parmesan.
Starting at one end, roll up and place each roll seam side down in the sauce, leaving a little room between them.
Top the rolls with the remaining sauce and sprinkle with the remaining mozzarella and parmesan cheese.
Bake uncovered for 30 minutes, serve warm.