Rinse the beef tongue under cold water and pat dry with paper towels.
Place the beef tongue in the slow cooker.
Add the onion quarters, smashed garlic cloves, bay leaves, black peppercorns, kosher salt, carrots, celery, and dried thyme to the slow cooker.
Pour the beef broth over the ingredients, ensuring the tongue is mostly submerged.
Cover the slow cooker with the lid and cook on low for 8 hours, or until the tongue is very tender and easily pierced with a fork.
Carefully remove the beef tongue from the slow cooker and let it cool slightly until it is safe to handle.
Using a sharp knife, peel off the thick outer skin of the tongue. It should come off easily once cooked.
Slice the peeled beef tongue into 1/4-inch thick slices.
Serve the sliced beef tongue warm with your choice of sides or use in sandwiches, tacos, or other dishes.