Preheat your oven to 425°F. While the oven heats, dice the carrots into 1/4-inch pieces, seed and dice the bell pepper into 1/2-inch pieces, dice the zucchini and onion into similar-sized pieces, and mince the garlic cloves. Having everything prepped and ready before cooking ensures you won't be rushed during the sauté phase.
Heat 2.5 tablespoons of olive oil in a large skillet over medium-high heat. Add the diced carrots, bell pepper, zucchini, and onion with 1/2 teaspoon salt, and cook for 8-12 minutes, stirring occasionally, until the vegetables begin to soften and develop light color. Add the spinach and cook for another 3 minutes, stirring frequently, until completely wilted. Transfer the cooked vegetables to a food processor.
Drain the canned diced tomatoes well to remove excess liquid. In a blender, combine the drained tomatoes, fresh basil leaves, 2 tablespoons olive oil, minced garlic, 3/4 teaspoon salt, 1/4 teaspoon red pepper flakes, and dried oregano. Blend until smooth but still slightly textured—you want some body to the sauce, not a completely puréed consistency. Set aside.
In the food processor with the cooked vegetables, blend 1 cup of the cottage cheese for about 1 minute until smooth and creamy. Add the remaining 16 ounces of cottage cheese, 1/2 teaspoon salt, and freshly ground black pepper to taste. Pulse the processor 5-7 times until the vegetables are finely chopped and well combined with the cottage cheese—you want a chunky texture, not a smooth paste. I find pulsing rather than continuous blending gives you better control over the texture and keeps the filling from becoming too dense.
Spread 1/2 cup of the tomato-basil sauce from Step 3 evenly across the bottom of a 9x13-inch baking dish. Arrange 3 parboiled lasagna noodles on top of the sauce. Layer half of the cottage cheese-vegetable filling from Step 4 evenly over the noodles, followed by 3/4 cup more sauce and 1/2 cup of the shredded mozzarella. Add another layer of 3 noodles, then the remaining vegetable filling, and top with 1/2 cup shredded mozzarella. Finish with the final 3 noodles, the remaining 3/4 cup sauce, and the remaining 1 cup shredded mozzarella spread evenly across the top.
Cover the assembled lasagna with aluminum foil and bake for 18 minutes. Remove the foil and continue baking for 10-15 minutes more until the cheese on top is melted and beginning to brown. Remove from the oven and let cool for 15-20 minutes—this resting time allows the lasagna to set so it will slice cleanly rather than fall apart. I like to tent it loosely with foil while it rests to keep the top warm. Top with fresh basil leaves if desired and serve.