Adjust the oven rack to the lower third position.
Preheat the oven to 325°F/160°C.
On the stovetop, heat the oil over medium heat in a 5-qt. Dutch oven. Season the short ribs with salt and pepper. In small batches, brown the ribs on all sides, turning only one time.
Remove the excess oil from the pan, leaving about 1 Tbsp. in bottom of the pan. Add the onions and garlic and sauté for 2 - 3 minutes until they are tender.
Add the tomatoes, parsley, thyme leaves and return the ribs to the pan. Add the beef stock and red wine and bring all to a simmer.
Cover with the lid and place in the oven for 1 1/2 hours.
Add the potato wedges and carrots and continue to cook uncovered for 30 minutes.
Add the green beans, gently mix them into the pan juices and cook for 10 minutes or until beans are tender. Ribs and vegetables should be tender. Serve.