Pat the short ribs dry with paper towel then season generously with salt and pepper on all sides.
Heat oil in a large, deep braising pot or a large Dutch Oven over medium-high heat.
Add the short ribs. Sear them in batches, to avoid overcrowding the pan, until they are deeply golden on all sides. Remove from the pan and set aside.
In the same pot, add the vegetables and fresh herbs then cook for 5 minutes until fragrant.
Add the garlic and tomato paste then pour in the wine. Allow to come to a simmer, deglazing the pot.
Stir in the beef stock then season with salt, pepper and a pinch of sugar.
Add the beef short ribs back into the pot then cover with a lid and place in the oven for 2-3 hours or until the ribs are fork tender. Check on them half way through cooking and add a cup or two more beef stock if necessary.
Once the short ribs are cooked, remove the pot from the oven. Remove the ribs from the sauce and set aside.
Strain out the solids then return the cooking liquid to the pot. Over medium heat, allow to come to a boil then reduce the heat and simmer for 15 minutes until the sauce has reduced a little.
Adjust the seasoning by adding a spoon of sugar, salt or pepper if necessary then add the ribs back to the sauce.
Serve the short ribs over risotto, creamy polenta or mashed potatoes.