Place tongue, garlic, onion, bay leaves, peppercorns, marjoram, thyme, oregano and 1 tablespoon salt in a casserole or soup pot. Cover with water up to 2 inches above the tongue.
Bring to a rolling boil over high heat, then reduce to a gentle medium simmer, cover with a tight fitting lid and cook for 3 hours, or until the tongue is completely tender and soft. Check the water halfway through and add more hot water if need be to keep the tongue mostly covered.
Turn off the heat. Let cool slightly in the liquid until you are ready to eat.
Remove the tongue from the broth and place on a chopping board. Using a small sharp knife and your hands, remove the outer layer of skin, as well as the bottom part of the tongue, which would attach it to the mouth, as it tends to be harder and greasy. The tongue is easier to peel if it is still warm or hot.
Slice into 1/4-inch slices and cut into about a 1/4-inch dice.
Heat oil in a medium-sized skillet over medium-high heat. Add 1/4 cup of the chopped onion and cook for a couple minutes, until softened. Incorporate diced tongue, season with salt and pepper to taste, and cook for about 4 to 5 minutes, stirring occasionally, until lightly browned and the onion has completely softened. Turn off the heat.
Heat corn tortillas on an already heated comal over medium heat. Make sure the tortillas are thoroughly heated and lightly browned on both sides. Place in a clean kitchen towel and wrap to keep warm, or keep in a tortilla warmer.
Place the tongue in a bowl and start assembling the tacos: spoon a generous amount of tongue in the middle of the tortilla, spoon a generous amount of salsa verde on top, and garnish with fresh chopped onion and cilantro. If desired, add a gentle squeeze of fresh lime juice.