Sauté the vegetables. Heat olive oil in a large skillet set over medium heat. To the heated oil, add the carrots, peppers, onions, and zucchini; season with salt and pepper and cook for about 8 to 10 minutes, or until the veggies are tender. Stir in the garlic and basil pesto; continue to cook for 1 more minute. Remove from heat and set aside.
Make the cheese mixture. In a large mixing bowl, combine the cottage cheese, feta cheese, basil, salt, and pepper; stir until completely incorporated.
Combine. Add the veggie mixture to the cheese mixture and stir until combined. Taste for seasonings and adjust accordingly. Set aside.
Layer. Spread ½ cup of marinara sauce on the bottom of a 9x9 baking dish. Layer 3 to 4 no-boil lasagna noodles in a single layer over the marinara sauce, snapping off the end pieces to fit in the baking dish.
Add the cheese mixture and marinara. Spread half of the cheese and veggie mixture evenly over the noodles. Then top with ¾ cup marinara sauce; spread it evenly.
Continue to layer. Sprinkle with ½ cup shredded mozzarella cheese. Layer 3 to 4 more lasagna noodles, then top with a layer of the remaining cheese and veggie mixture. Sprinkle with ½ cup shredded mozzarella cheese.
Finish layering. Top with remaining lasagna noodles. Spread ¾ cup of marinara sauce on top of the noodles. Sprinkle with remaining shredded mozzarella cheese and grated parmesan cheese.
Bake. Cover with foil and bake for 30 minutes. Remove the foil and continue to bake for 10 more minutes, or until the cheese is melted and the top is lightly browned.
Rest and serve. Remove the lasagna from the oven and let it rest for 15 minutes. Garnish with basil, cut, and serve.