Heat 2 tablespoons of the olive oil in a large heavy skillet.
Add the onions and cook, uncovered and stirring, over low heat for 10 minutes. Add the cinnamon, stir, and continue to cook for another 4 to 5 minutes. The onions should be tender and slightly caramelized. Remove and wipe the skillet clean.
Heat 2 more tablespoons of olive oil and cook the carrots, uncovered and over low heat, stirring occasionally, until tender but al dente, about 15 minutes.
Preheat the oven to 375℉ (190℃). In a large pot, bring 5 cups of salted water to a rolling boil and add orzo. As soon as the water begins to boil again, remove the pot from the heat and pour contents into a large ovenproof casserole or earthenware dish. Add the onions, carrots, tomatoes, 2 tablespoons of olive oil, bay leaves, oregano sprigs, salt and pepper and toss to combine. Cover and bake 20 to 25 minutes, stirring up the mixture every 7 to 10 minutes to keep the orzo from sticking to the bottom of the dish.
Meanwhile, heat 2 more tablespoons of olive oil in the skillet and cook the zucchini until tender but firm, about 8 minutes. Add the garlic and stir for 1 minute. Toss the zucchini and garlic in with the orzo, combining well. Uncover the pan and continue to bake for another 50 minutes to 1 hour, until the orzo is tender. Check the orzo and stir it during baking to prevent it from sticking. You may have to add additional water, as well.
Just before serving, remove bay leaves and oregano and mix in remaining olive oil and balsamic vinegar. Served hot, sprinkled with grated cheese, if desired