Select a ceramic, glass or enameled crock or bowl large enough to hold both the tongue and enough brine to cover the tongue by two or more inches. Be sure the container will fit in the refrigerator. To determine the brine quantity needed, enclose the tongue in a plastic bag and run cold water into the container to cover the bagged meat by two to three inches. Remove the tongue. Stir kosher salt gradually into the water, dissolving thoroughly each time, until an egg will float in it. (This will run about a cup and a half of salt.) Remove the egg once it's served its purpose and pour the brine into a pot. Stir all the other ingredients into the brine and bring to a boil, then simmer, covered, for 15 minutes. Let brine cool completely.
Remove the tongue from the plastic bag and prick it well all over with a skewer or larding needle. Return to the crock. Once the brine has cooled, pour it over the tongue. Cover with Saran, then add a plate (weighted, if need be) to keep the meat well under the surface. Cover the whole crock with Saran and refrigerate for 10 days to 2 1/2 weeks (allow three days a pound curing time).
Turn the meat every few days, and be sure to keep it always sunk in the brine. To cook: Put the tongue in a pot with water to cover by several inches, two or three carrots coarsely chopped, a whole onion or two (peeled), a few tablespoons of vinegar, and simmer, partly covered, until the meat is very tender. Remove from the stock, and slit the skin and peel it away. Serve hot or cold.