Sear the ribs Season the pork ribs with salt and pepper. Heat olive oil in a large Dutch oven over medium-high heat and sear the ribs on all sides until browned. Remove and set aside.
Build the sofrito In the same pot, add onion, carrot, and celery. Cook until softened and fragrant, about 5–7 minutes. Stir in the garlic and cook for another minute.
Deglaze Pour in the white wine, scraping up any browned bits from the bottom of the pot. Let it simmer for 2–3 minutes to reduce slightly.
Braise Return the ribs to the pot and add the tomato sauce. Cover and reduce heat to low. Let simmer gently for 1½ to 2 hours, or until the ribs are tender and nearly falling off the bone.
Finish and serve Sprinkle with fresh parsley before serving. Spoon the sauce over the ribs and serve hot.