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. Stir until wilted. Repeat with remaining spinach until all has wilted, about 3 minutes. Remove from heat.
In another bowl, pour the tomatoes into a mesh sieve to drain excess juice. Transfer to a food processor. Add basil, olive oil, garlic, salt, and red pepper flakes. Pulse until spreadable.
Transfer the mixture to a bowl for later. Rinse out the food processor.
Blend half of the cottage cheese (1 cup) until smooth. Transfer to a mixing bowl.
Pulse the cooked veggies and spinach in the food processor until finely chopped. Transfer to the bowl of cottage cheese. Top with remaining cottage cheese, salt, and pepper. Stir to combine.
Spread ½ cup tomato sauce in the bottom of a 9” by 9” baking dish. Layer 3 lasagna noodles, half of the cottage cheese mixture, ¾ cup tomato sauce, and ½ cup mozzarella cheese on top.
Top with 3 more noodles and remaining cottage cheese mixture. Sprinkle with ½ cup mozzarella cheese.
Top with 3 more noodles and spread ¾ cup tomato sauce over the top. Sprinkle with 1 cup mozzarella cheese.
Cover with parchment or foil and bake for 18 minutes. Remove cover, rotate, and bake for 10 to 15 more minutes until top is spotty brown.
Let cool for 15 to 20 minutes. Sprinkle additional basil, slice, and serve.