Place the short ribs in a dish large enough so they fit in a single layer. In a bowl, combine the minced garlic, wine, Dijon, oregano, thyme, rosemary and 2 tbsp (30 mL) of the olive oil and pour over the short rib. Set the short ribs aside to marinade for 2 hours.
Preheat oven to 225°F (110°C).
Remove the ribs from the marinade, reserving the marinade. Pat dry the ribs and season with salt and pepper.
Heat the remaining 2 tbsp (30 mL) of olive oil in a large skillet or Dutch oven over high heat. Working in batches, brown the ribs, about 2 to 3 minutes per side. Set aside.
Remove all but 1 tbsp (15 mL) of oil and reduce the heat to medium. Add the shallots and sauté until they pick up some colour about 2 minutes. Add the beef stock, Worcestershire, soy sauce and reserved marinade and bring to a boil, stirring to combine, scraping up any browned bits from the bottom of the pan. Return the short ribs to the pan, cover, and place in the oven. Bake for 31/2-4 hours, or until ribs are fork-tender.
While the ribs are braising, prepare the mushrooms for the sauce. Heat 1 tablespoon each of butter and olive oil in a pan over high heat. Add the sliced mushrooms and sauté until lightly browned, about 5 minutes. Season with salt and pepper and set aside until the ribs are cooked, and you are ready to finish the sauce
Transfer the tender short ribs from the pan to a warm serving dish and let them rest.
Skim any fat from the sauce, then cook over medium heat until slightly thickened, about 5 minutes. Add the mushrooms to the sauce to rewarm.
Serve the short ribs over mashed potatoes or celery root, with a little of the sauce poured over top and extra sauce alongside.