In a medium covered skillet, cook carrots, onion, and garlic in about 1 1/2 tsp oil till onion is tender but not brown.
Stir in the pasta sauce, water, oregano, and basil; simmer covered 15 minutes or until carrots are tender.
Stir in the mushroom and zucchini into the skillet; cooked uncovered about 5 minutes or till zucchini is tender.
Meanwhile, using a wire stainer, squeeze any remaining liquid from the thawed spinach with a metal spoon.
In a bowl stir together the spinach, eggs, cottage cheese and parmesan.
Arrange a single layer of cooked lasagne noodles on the bottom of a greased 12 x 7 1/2 x 2-inch baking dish; top noodles with 1/3 of spinach mixture, spread with 1/3 of the sauce mixture, add with 1/2 cup mozzarella cheese, top with add 1/3 of the vegetable mixture - REPEAT layers 2 more times.
Bake uncovered in a 375°F oven 35 minutes or till heated through.
Top lasagne with 2/3 cup mozzarella; return to oven for 3 minutes or until top cheese has melted.
Let stand 10 minutes before serving.