Step 1The day before cooking, season the ribs with the salt, pepper and garlic powder. Cover with plastic wrap and refrigerate overnight.
Step 2Heat the oven to 325 degrees. Heat the olive oil in a roasting pan over medium-high heat until hot but not smoking. Add the ribs and brown on all sides, about 1 minute per side. Remove from the pan and set aside.
Step 3Discard all but 2 tablespoons of the fat from the pan. Add the onion, celery, carrot. Cook, stirring often, until lightly browned, about 8 minutes. Add the wine, vinegar, broth, thyme and bay leaf. Stir in the mushrooms. Bring to a boil over high heat.
Step 4Return the ribs to the pan, cover with foil and braise in the oven for 1 hour. Remove the foil and cook 3 more hours, or until the meat is very tender and falling off the bone.
Step 5To serve, remove the ribs from the braising liquid and divide among 6 warm, shallow bowls. (Leave the bones for a dramatic presentation.) Remove the mushrooms and reserve. Strain the braising liquid, discarding the solids. Skim off and discard the fat from the liquid. Add the reserved mushrooms back in and pass as a sauce at the table.