In a saucepan, combine the rice and water. Bring to a boil. Cover and reduce heat to low. Simmer for 15 to 20 minutes, until water is absorbed and rice is tender.
Meanwhile, heat the olive oil in a large pot. Add the onion and garlic; cook and stir until fragrant, about 3 minutes. Add the cabbage, and cook for about 10 minutes, stirring occasionally, until the cabbage cooks down. Mix in the tomatoes, pepper rings and cooked rice. Simmer for 10 to 15 minutes to blend the flavors together.
