Place the tongue, half of the chopped onion, garlic cloves, 3 tablespoons salt, and 1 jalapeno pepper into a large pot. Fill with water to cover the tongue by several inches, then bring to a boil over high heat. Reduce heat to medium-low; cover and simmer until very tender, 3 to 4 hours. Remove the tongue from the water and allow to cool. Reserve the liquid. Once the tongue has cooled, peel off the tough outer skin, then shred the meat using two forks.
Bring a large saucepan of water to a boil over high heat. Add the whole tomatoes and 2 jalapeno peppers; boil until the vegetables are tender. Place the vegetables into a blender, and puree until smooth. Heat the vegetable oil in a large skillet over medium heat. Stir in the onion, and cook until the onion has softened and turned translucent, about 5 minutes.
Once the onion has softened, stir in the shredded beef tongue and tomato salsa. Bring to a simmer, stirring occasionally, then pour in 2 cups of the reserved cooking liquid. Cook and stir until the liquid has evaporated, leaving moist, flavorful meat, about 20 minutes.
