Heat 2 tablespoons of the oil in a Dutch oven over medium-high heat. Brown the ribs on all sides, working in batches if needed.
3 tbsp vegetable oil
Remove the browned ribs and set them aside.
Add the remaining 1 tablespoon of oil to the Dutch oven and reduce the heat to medium. Add the carrots, celery, onions, and mushrooms.
Sauté until vegetables are soft, about 5 minutes.
Add the garlic and cook while stirring until fragrant, about 1 minute.
4 cloves garlic
Add the tomato paste and cook while stirring for about 3 minutes.
2 tbsp tomato paste
Deglaze the pan with the wine.
½ cup dry white wine
Add the vinegar.
1/4 cup white vinegar
Add the bay leaves and cayenne pepper. Scrape up any bits from the bottom of the Dutch oven (the fond), to incorporate the flavor back into the sauce.
2 bay leaves, 1/4 tsp cayenne pepper
Add the ribs back to the pan.
Add enough chicken stock to barely cover the ribs.
2 1/2 cup chicken stock
Bring the sauce to a simmer.
Cover and place in the oven. Braise until the meat is tender, about 1 1/2 hours.
During the last half hour, uncover to allow the liquid to reduce and the pork to brown.
Add a generous hunk of meat and several mushrooms to a bowl of white rice, polenta, mashed potatoes, or egg noodles. Ladle some of the sauce over the top. Enjoy!