To a pot large enough to comfortably fit the tongue, submerge the tongue in water. Add the peppercorns and bay leaves. Cook for an hour and a half. Cool well and place in the refrigerator overnight.
The next day, slice it with a sharp knife. Strain and reserve three cups of the cooking liquid.
In a wide, flat pot, fry the onion in oil. Add mushrooms and cook about another 10 minutes. Add the remaining seasonings, a little more oil, and reserved cooking liquid. Bring to a boil and add the pieces of tongue. Shake the pot in a circular motion once in a while. Add water to just cover the vegetables and meat.
Lower the heat and cook for about two hours.