Heat the oil in a heavy-bottomed 2-quart saucepan over medium heat. Add half the onions and cook, uncovered, stirring occasionally, until the onions are caramelized but do not burn, about 5 to 10 minutes. Add the remaining onions, the sausage, green pepper, celery and garlic. Cook, stirring frequently, for 5 minutes. Add the rice and stir to coat with oil. Add the tomatoes, oregano, Tabasco sauce, thyme, cayenne, bay leaf and chicken broth. Bring to a boil over high heat, cover, reduce the heat and cook until liquid is absorbed and rice is tender, about 25 minutes. Add the shrimp, cover and cook an additional 5 minutes over low heat, or until the shrimp are pink. Taste and adjust seasoning.