Prepare the tongue. Rinse the tongue thoroughly under running water. If using a whole tongue, wrap and freeze any portion you’re not cooking. Optional: trim excess fat or score the surface to make peeling easier after cooking.
Simmer with aromatics. Place the tongue, vegetables, and seasonings in a medium stockpot. Add stock and water (or all water). Bring to a boil, skimming foam, then reduce to a gentle simmer. Cover and cook 30 minutes, tasting the broth—add salt if it tastes flat.
Cook until tender. Simmer for 1½–2 hours (beef tongue closer to 2 hours) until fork-tender. If still tough, continue cooking in 30-minute increments. Lift the tongue from the broth and let it rest until warm enough to handle. Save the broth for soups or sauces.
Peel the skin. While still hot, peel off the outer skin starting at the tip—it should come off easily in one piece.
Trim and chill. Trim the underside of the tongue if desired. Place the remaining tongue in a covered container and refrigerate until firm, making it easier to slice.
Slice and serve. Use a sharp knife to cut the chilled tongue into thin slices. Perfect for sandwiches, tacos, salads, or any dish that calls for tender, flavorful beef.