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Heat 2 tablespoons of the olive oil in a large heavy skillet.
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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.
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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.
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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.
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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.
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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