Season the ribs generously with salt and pepper.
Heat a large stock pot with olive oil over medium-high heat.
Working in batches, add as many ribs as you can to the pot and sear them on all sides. Then set them aside on a platter to rest while you work on the braising liquid.
Add the diced onion, celery, and carrots to the stockpot. Stir from time to time while they cook.
When the veggies are softened, add the tomato paste, chopped garlic, salt, and pepper. Stir it together, allowing the garlic to become fragrant and the tomato paste to darken in color. This will add depth to the flavor of the braising liquid.
Add the red wine, tomatoes, bay leaves, and dried herbs. Stir to combine, then carefully add the seared ribs to the pot. Add enough beef broth or stock to cover the meat.
Put the lid on the stock pot and turn the heat to low. Continue to simmer for an hour and a half or until the meat is tender and pulls away from the bone easily.
Alternately, the covered stock pot can be placed in a preheated oven at 325 degrees or you may transfer the contents of the stock pot to a crockpot set on low heat (or the oven equivalent of 325), and the ribs can finish simmering with those methods.
Transfer to a serving platter, sprinkle with fresh parsley if you’d like, and serve with your favorite bread, rice, pasta, or mashed potatoes.