In a deep saucepan, heat 2 tablespoons of the olive oil over medium heat and saute the onion until very soft, about 5 minutes. Add the zucchini and saute a minute or two to soften. Add the tomato puree, tomato paste, and oregano. Bring to a boil, then simmer, uncovered, for 15 minutes.

In a medium-size saucepan, bring the 3 1/2 cups of water to a boil. Add the remaining 1 tablespoon olive oil. Add the rice, cover, and cook until the water is absorbed and the rice is tender, 20 minutes.

In a large skillet over medium heat, cook the sausage with the 3 tablespoons water. Cover and cook for 5 to 7 minutes, until lightly browned, breaking it apart as it cooks. Remove the sausage with a slotted spoon, draining off any fat, and add it to the tomato sauce. Season with salt and pepper. Cook the sauce for 10 more minutes, or until the rice is done.

Ladle the rice into shallow bowls, top with some sauce, and pass the cheese at the table.