How to Make It
In a large enameled cast-iron casserole, heat the canola oil. Season the veal shanks with salt and pepper and brown them in the oil over moderate heat, about 7 minutes per side. Transfer the veal to a plate. Add the onion, carrot and celery to the casserole and cook, stirring, until softened but not browned, about 5 minutes. Add the chicken stock and bring to a boil, scraping up any browned bits from the bottom of the casserole.
Return the veal shanks to the casserole and add the bouquet garni. Cover and cook over low heat until the meat is very tender, about 1 1/2 hours.
Meanwhile, in a large skillet, melt the butter in the olive oil. Add the mushrooms and season with salt and pepper. Cook over moderately high heat until the mushrooms are dry and just beginning to brown, about 10 minutes. Add the garlic and thyme and cook until fragrant, about 2 minutes longer.
Transfer the veal shanks to a platter; when cool enough to handle, discard the bones and gristle. Strain the cooking liquid, pressing hard on the solids. Return the liquid to the casserole and boil until it is reduced to 2 cups, about 20 minutes. Return the veal to the sauce, add the mushrooms and cook over low heat just until warmed through. Serve hot.