You do not keep the salt water in which you boiled the tongue. It's been over 60 years, so the details are a mite hazy. I do remember that after Mom boiled it and let it cool enough to handle, she removed the outer skin, leaving just the smooth inner muscle. Then sliced it maybe a quarter inch thick, on an angle to get the widest slices. We usually ate it as sandwich meat with a smear of mustard.
Mexicans do it similar.
Quarters onion and some garlic cloves in a pot of salted water. Boil it, then skin it. Sliced or chopped.
Makes killer tacos.
