Heat the oven to 375°F. Cook the noodles according to the package directions, then drain them and lay them flat.
Mix the ricotta, egg, spinach, zucchini, ½ cup mozzarella, Italian seasoning, and salt in a bowl.
Spread 1 cup of marinara in a 9-by-13-inch baking dish. Add a few spoonfuls of filling to each noodle, roll them up, and place them seam-side down.
Spoon the remaining sauce over the rolls and sprinkle on the remaining mozzarella.
Cover with foil and bake for 25 minutes. Remove the foil and bake 5 minutes more, until the cheese melts.