Boil with a tablespoon of salt, a pinch of pepper and a pinch of oregano until they are very tender. A pressure cooker will help speed up the process. Remove from the water and reserve the water in which they boiled. Pat dry the gizzards with a paper towel.
Heat the oil in an large deep bottomed pot. Add the gizzards, taking care with splattering oil. Brown lightly and add green peppers, peas, garlic, thyme, olives, celery, auyama and cilantro.
Simmer over low heat until the vegetables start to wilt. Add tomato sauce and stir to combine. Add water, increase heat to medium and bring to a boil. Season with salt. Add the rice and stir often to prevent it from sticking to the pot.
Once all the water has evaporated, cover with a tight-fitting lid and simmer over very low heat. Wait 15 minutes, uncover and stir. Cover and wait another 5 minutes.
Taste rice for "doneness"; it should be firm but tender inside. If necessary, cover and leave another 5 minutes over very low heat.
As I include more recipes in our collection I am adding the more obscure ones (although not unknown to Dominicans), like this recipe. Unlike many places, where gizzards, along with other viscera, are considered an inedible byproduct, in the Dominican Republic it is a delicacy.Unless you are a talented masticator, set aside enough time for cooking this, gizzards are the toughest muscles in poultry.