Preheat the oven to 400°F and arrange the rack to the center position. Spray a 9x13-inch casserole dish with non-stick spray.
Heat the olive oil in a large skillet over medium-high heat. Add the onion, garlic, zucchini, mushroom, and carrots, and cook to soften, 5-6 minutes. Add the spinach and cook to wilt. Turn the heat to low, add the balsamic vinegar and continue to cook for 3-4 minutes, until the veggies are soft and the moisture is reduced. Remove from heat.
In a separate large bowl, combine the cottage cheese, parmesan cheese, garlic, salt and pepper.
To assemble the lasagna, spread 1 cup of the marinara in the bottom of the pan, then layer with 3 lasagna noodles, half the cottage cheese mixture, half the veggie mixture, ⅓ of the shredded cheese. Repeat with another layer of the marinara, noodles, cottage cheese, veggies and shredded cheese. Finish with a final layer of noodles, marinara, and shredded cheese.
Cover with foil and bake in the preheated oven for 30 minutes, then uncovered for 10-15 minutes, until the edges are bubbling and the top is golden brown.
Allow to cool for 15-20 minutes before slicing. Top and serve with parmesan cheese, red pepper flakes, or fresh parsley.