Toss the livers, 1 teaspoon of olive oil and a dash of salt and pepper in a glass or stainless bowl. Place the livers on a baking sheet with sides and place it on top rack of the oven. Bake them for 20 minutes. Cool the livers and finely chop; set aside.
Heat the remaining 2 tablespoons of olive oil in a heavy-bottomed, oven-safe saucepan over medium heat. Add the onions and garlic and saute, stirring for 2 to 3 minutes until the onions become translucent. Add the sausage, cook and breaking into small pieces, about 4 minutes. Add the Tasso and chicken livers and saute for about 3 minutes. Add the rice and stir until the rice is coated by the olive oil. Add salt and pepper, to taste. Note: Before salting, take into consideration the Tasso and sausage contain salt, as may the broth.
Pour in the chicken broth and bring the mixture to a boil, stirring constantly. Cover the saucepan and place it in the oven. Bake the rice for 20 to 30 minutes or until all of the liquid is absorbed and the rice is tender. Uncover the saucepan, add the green onions and fluff the rice and onions with a fork.