Take short ribs out of the refrigerator and out of the package. Let them rest and warm up on the cutting board, on the counter, for about 30 minutes before cooking.
Slice onion, dice carrots, and celery and set them aside. Peel the outer loose skin of garlic and cut off just the tips to expose the garlic flesh.
Pat the ribs dry with a paper towel and season generously with salt and pepper on all sides.
Season and sear:
Preheat a large Dutch oven over medium-high heat. Add canola oil.
Sear the ribs in batches of 3 or 4 so they are not overcrowded. Sear them on all 4 sides until golden brown.
Take them out and set aside. (If there is a lot of excess fat from searing the ribs, drain it off.)
Cook vegetables and make the sauce:
Preheat the oven to 325° and remove the middle rack in needed, to be able to fit the Dutch oven.
Sautee the onion, carrots, and celery in the same pot until softened and golden. (Add a little more canola oil if needed.)
Add garlic bulb cut side down and let it sear for a few seconds.
Pour in the bottom of wine while slowly stirring and scraping the bottom of the pot.
Add ribs back into the pot and lower the heat to medium. Let the ribs simmer in red wine for about 10 minutes.
Whisk together beef stock, tomato paste, and herbs and pour it into the pot.
Stir everything carefully and cover with a lid.
Cook In The Oven:
Transfer the Dutch oven into the preheated oven and cook for 2 1/2-3 hours.
Take off the lid and cook another 30-40 minutes. (Until the rib meat is completely tender.)
Prepare sauce:
Carefully take the ribs out of the pot and set them aside. (It's okay of they fall off the bone, they are supposed to.)
Strain the sauce through a large fine mesh strainer. Stir the vegetables in the strainer to extract the juices and discard what is left in the strainer.
Add the ribs back into the pot with the sauce. You can spoon the excess fat from the surface of the sauce or you can do it the next day while it's cold.
Tips:
You can serve the ribs right away or the next day. It's actually better the next day and you will have a chance to get rid of the excess fat easily.
To get rid of the excess fat, refrigerate the cooled ribs in sauce. While it cools, the fat layer on the top will harden. You can easily take it off with a spoon the next day and discard.