Preheat the oven to 200 degrees Celsius (390 degrees Fahrenheit)
Season the short ribs on all sides with salt and pepper. Heat the olive oil on high heat in a large oven proof pot and then sear the short ribs for 3-4 minutes per side until browned. Once they are seared on all sides transfer them to a plate and set aside.
Add to the pot the onion, leek, garlic and carrots and cook for 5 minutes until the veggies begin to soften. Next add in the tomato paste, balsamic vinegar, beef stock, thyme, chopped tomatoes and bay leaves and bring the mixture to a boil.
Once boiling, return the short ribs back to the pot cover with a lid and place in the oven to cook for 2 1/2-3 hours until the meat is fall of the bone tender.
Once the meat is done cooking, return the pot to the stove top. Remove the short ribs from the pot and set them aside on a plate. Bring the pot to a boil and let it cook on high heat for 10 minutes until the liquid has reduced by half.
At this point you can serve the sauce as it, or alternatively using an immersion blender, remove the pot from the heat and blend the sauce until its completely smooth.
Serve the short ribs with the sauce and a side of mash