Scrub the tongues clean under running water, then place them in the slow-cooker and cover with water. Cook on low for 5-6 hours or until easily pierced with a knife.
Drain the water. While the tongue(s) are still hot, cut a slit in the top of the tongue near the tip and peel the leathery skin and thin membrane underneath back. Peel the skin off and cut away any gristle you find on the underside of the tongue.
Return the tongues to the slow-cooker and add the remaining ingredients. Slow-cook on low for 8 hours, then shred before serving.