Browning meat: Heat a 3 quart [3 lt] pot over high heat. Add pork chops and brown (see notes). You can cover to avoid splatters, but stir often to cook evenly.Remove excess fat if you find it necessary. Not all pork chops have the same amount of fat.
Cooking the vegetables: Lower heat to medium. Stir in onion, celery, bell pepper, garlic, oregano, capers, and olives. Once the vegetables have been heated through, add thyme and tomato sauce and stir.Add beans, also while stirring. Add water and bring to a boil. Taste and season with salt if you find it necessary (I did not, the pork chops were plenty salty).
Cooking the rice: Add the rice and stir regularly to avoid excessive sticking. Make sure to remove the rice that sticks to the bottom.When the water has evaporated cover with a tight-fitting lid and simmer over very low heat for 15 minutes. Uncover and stir, moving the rice at the bottom to the top.Cover again for another 15 minutes. After this, the rice should be firm but tender inside. If necessary, cover and leave another 5 minutes over very low heat. Discard the thyme twigs.
Serving: Serve with salad and avocado or tostones.
If you want, you can use most smoked pork cut with bones (like chops, ham hock, ham, etc).Some meat products (like pork chops) have enough fat that no oil is needed to brown them. Brown in 2 tablespoons of oil if you use slim meat.If you have experience cooking Dominican rice it may look to you that we're adding too little water, but remember that the tomato sauce has water, and also the vegetables release water too, so no more is needed.