Fill a large (12-quart if you have one) stock pot two-thirds full with water. Add the tongue, onions, crushed garlic cloves, bay leaves, peppercorns, and salt. Bring to a boil, reduce to a simmer, cover, and cook for 3 hours, until the tongue is soft to the touch and tender.
Remove tongue from water and let cool for a couple of minutes. Notice the light colored skin-like covering over most of the tongue. Using your fingers, and/or a sharp small knife, remove this covering and discard. Notice the rough patch of meat where the tongue would attach to the bottom of the mouth. Arturo removes this patch (as does his mother when she prepares tongue) because it is a little rough. It's perfectly edible though, so keep it attached if you want.
Slice the tongue in 1/4-inch slices. (If you are not preparing the whole tongue for tacos, you can return whatever tongue you do not slice to the cooking water to soak.) Heat a little oil in a frying pan on medium high and sauté the slices on both sides until they are lightly browned. Remove from pan and slice first into strips, then crosswise again so that you end up with small cubes.
Soften tortillas either by cooking on the stove-top until pockets of air appear in them, or in the microwave (about 10 seconds per tortilla). Place a large spoonful of meat in the center of a tortilla. Add a spoonful of salsa verde and some chopped avocado, chopped fresh cilantro.