Cut the zucchini in half lengthwise. Using a melon baller, scoop the pulp out of each zucchini half, leaving an 1/8-inch-thick shell. Dice the pulp and reserve the zucchini shells.
Heat the oil in a 10-inch skillet over medium heat. Add the onion, carrot and zucchini pulp and cook until the vegetables are tender, stirring occasionally. Stir in the rice and 1 cup sauce and cook until the mixture is hot and bubbling.
Spoon the vegetable mixture into the zucchini shells. Place the filled shells into a 2-quart shallow baking dish. Top with the remaining sauce. Sprinkle with the oregano and cheese.
Bake at 400 degrees F for 30 minutes or until the zucchini shells are tender.