Heat onion, celery, carrot, garlic cloves, thyme, bay leaves and wine in saucepan over high heat. When the mixture comes to a boil, the wine may ignite (this is supposed to happen, to burn off the alcohol). If it does not ignite on its own, carefully ignite with a lighter. Either way, the flames will extinguish themselves when the alcohol has burned off. The goal is to remove the bitterness of the alcohol from the braise, yet retain the flavors of the wine. After the flame has gone out, allow the mixture to cool, then pour over the short ribs that have been placed in a roasting pan. Cover and marinate for 8–24 hours, turning ribs, if necessary, to expose to marinade.
Remove the ribs from the wine and vegetable mixture and pat dry with towels. Strain the vegetables from the wine, reserving both the vegetables and the wine.
Preheat oven to 275°F. Heat canola oil in heavy-bottomed pan until just smoking. Generously season the short ribs on all sides with salt and pepper and place the ribs in the hot pan, being careful not to burn yourself (you may need to do this in 2 batches—do not crowd the ribs). Reduce heat to medium and continue to cook until all sides are golden brown. Remove browned ribs from the pan and place in high-walled roasting pan.
Next, sauté the reserved vegetables in the same pan in which you browned the ribs (in the same oil, adding a bit if necessary) until caramelized. Pour the caramelized vegetables over the ribs, then add the reserved wine and enough warmed veal stock or water to completely cover the ribs. Cover with parchment paper or aluminum foil and place in the preheated oven for approximately 4–5 hours, or until the meat is loose but not falling apart. Using a slotted spoon, remove the ribs from the braising liquid. Strain the vegetables out of the braising liquid, reserving the liquid. Discard the vegetables. Cook the braising liquid over medium-high heat in a saucepan until it has been reduced down to the consistency of a sauce, skimming the surface of fat periodically during this process.
Cut the ribs into the desired portion size and place in 400° oven, on lightly oiled sheet pan, for about 10–15 minutes until slightly crisp on the edges and warm inside. Place a portion of ribs on each plate and top with a spoonful of the reduced sauce.
Suggested side dishes: buttered pappardelle pasta, risotto or potato purée work well as a starch; sautéed curly kale or roasted root vegetables are great complements for a winter vegetable.