Preheat the oven to 425 degrees Fahrenheit.
In a large skillet over medium heat, warm the olive oil. Once shimmering, add the carrots, bell pepper, zucchini, yellow onion, and salt. Cook until the veggies are golden on the edges, about 8 to 12 minutes.
Add a few large handfuls of spinach and cook until wilted. Repeat with remaining spinach, about 3 minutes. Remove from heat.
Pour the tomatoes into a mesh sieve or fine colander and drain off excess juice. Transfer drained tomatoes to a food processor. Add basil, olive oil, garlic, salt, and red pepper flakes, and pulse 10 times until spreadable.
Pour the mixture into a bowl. Rinse the food processor and return it to the machine.
Blend half of the cottage cheese until smooth. Transfer to a large mixing bowl.
Pulse the cooked veggies and spinach until finely chopped, then combine with the whipped cottage cheese. Season with salt and black pepper.
Spread ½ cup tomato sauce over the bottom of a 9” by 9” baking dish. Layer 3 lasagna noodles on top, followed by half of the cottage cheese mixture, ¾ cup tomato sauce, and ½ cup shredded cheese.
Add 3 more noodles, the remaining cottage cheese mixture, and sprinkle ½ cup shredded cheese on top.
Top with 3 more noodles, spread ¾ cup tomato sauce over the top, and sprinkle evenly with 1 cup shredded cheese.
Cover with parchment paper or foil and bake, covered, for 18 minutes. Remove the cover, rotate the pan, and continue cooking for about 10 to 15 more minutes, until the top is spotty brown.
Remove from oven and let cool for 15 to 20 minutes. Sprinkle with additional basil, slice, and serve.