Preheat your oven to 325 °F (160 °C).
Heat a large heavy skillet over medium-high heat and add oil to cover the bottom with a light film. Add the ribs in a single layer and brown, caramelizing them well on all sides.
Be patient when you’re browning the meat; it takes a little time but it’s worth every minute. The caramelized flavours are the secret to a rich hearty braise. Because the majority of the ribs’ cooking time happens slowly while the beef is submerged in liquid, browning the meat is the only chance you have to add the deep rich flavours of caramelization.
Place the browned ribs on a platter, drain most of the fat from the pan and place it back over the heat.
Add the onions, celery, carrot and garlic to the hot pan and sauté for a few minutes until they heat through and smell great. Add the ribs back to pan and cover with wine. Add the rosemary and bay leaves and season well with salt and pepper.
Cover with a tight-fitting lid, or with tightly sealed foil and place in the oven to braise for about 2 hours. The ribs are done when they’re fork-tender and nearly falling off the bone.
Serve with your favourite mashed potatoes and the braising liquid.