This recipe was developed for a pressure cooker, but I've written it here in its conventional form, seeing as a pressure cooker is not a cooking appliance that many people have on hand. If you are one of the lucky ones to own a pressure cooker, follow the recipe exactly as you would but refer to your pressure cooker's manual for cooking time and temperature.
Preheat the oven to 375.
In a large Dutch oven, heat the canola oil to high heat. Brown the short ribs in batches so not to crowd the pan, about 4 minutes per side, and reserve on a plate when done. When all of the short ribs are done browning, add the olive oil to the pan and heat over medium-high. Cook the onion and garlic over medium heat until the onion is soft, about 5 minutes. Add the red wine, scraping up the brown bits from the pan as you go. Reduce the red wine by ¼, then add the beef broth, celery, carrots, thyme, and brown sugar. Return the short ribs and any collected juices to the post and bring to a boil. Once at a boil, remove from heat, cover, and cook in the oven to 3 hours until tender.
Halfway through the cooking time, check the ribs and add more liquid if they become too dry. When the short ribs are tender and falling off the bone, remove from the pot and cover with aluminum foil to keep warm. Boiling the braising liquid until thickened and serve with the short ribs and vegetables.