Rinse the tongue and place it in a large stockpot. Add enough water to cover it completely - I typically use 14 cups of water.
Bring the water to a boil. This should take about 20 minutes. When the water starts boiling, skim the foam off the top with a spoon. Lower the heat to a simmer. Add the bay leaves, peppercorns, and allspice.
Cook partially covered, turning the tongue every hour with two wide spatulas to ensure even cooking on all sides. Cook 3 hours for a 2-pound tongue and 4 hours for a 3-pound tongue.
Make the sauce:
Start making the sauce about 30 minutes before the tongue is ready. Heat the butter in a large, deep skillet over medium heat. Swirl to coat. Add the onions and cook, stirring occasionally, until golden, for about 10 minutes.
Add the mushrooms and cook, stirring, until soft, for about 5-7 minutes. If the pan becomes too dry, add a splash of broth.
Add salt, pepper, and beef broth. Bring to a boil over high heat. Lower the heat to a simmer, and cook, uncovered, for about 20 minutes to thicken the sauce and meld the flavors.
Mix the cornstarch with 2 tablespoons of water. Add this slurry to the sauce and stir until the sauce thickens. Turn the heat off, cover, and keep the sauce on the warm burner while you tend to the tongue.
Finish the dish:
Remove the cooked tongue to a cutting board. Allow it to cool for a couple of minutes until it is easier to handle, and then use your hands to peel off the skin.
Slice the tongue.
Arrange tongue slices on plates. If not using the sauce, sprinkle them with salt to taste (they were cooked in unsalted water to keep the meat tender). If using the sauce, spoon sauce on top of each slice, sprinkle the dish with chopped parsley, and serve.
Video
Notes
The nutrition info assumes a 2-pound raw tongue yielding about 1.5 pounds (24 ounces) of cooked meat. A 3-pound tongue should yield about 2 pounds of cooked meat.
The cooking liquid is rich and delicious and can be strained and used as a drinking broth. Salt it to taste.
Let the cooked tongue cool a little before removing the skin. It's too hot to handle when you remove it from the saucepan. But don't let it sit and cool for too long. Remove the skin as soon as you can. If it cools down too much, the skin becomes difficult to remove.
You can keep the leftovers in a sealed container in the fridge for 3-4 days. Reheat them, covered, in the microwave at 50% power, or enjoy them cold, thinly sliced (like roast beef), with veggies, pickles, and mustard.
You can also freeze the cooled leftovers in a freezer bag for up to three months. Thaw them overnight in the fridge and reheat them covered in the microwave.
If you made the sauce, you can keep it in a sealed container in the fridge for up to 4 days. Reheat it gently, covered, in the microwave at 50% power. I don't recommend freezing the sauce.