Rinse the tongue thoroughly. Place it in a large pot with chopped onion, garlic, bay leaves, salt, and pepper.
Cover with water and bring to a boil. Reduce heat and simmer for 2–3 hours, until the tongue is tender.
Remove the tongue and allow it to cool slightly. Peel off the tough outer skin while warm.
Slice the tongue thinly across the grain.
To make the sauce, melt butter in a small saucepan. Add mustard, sugar, and vinegar, stirring until smooth. Adjust seasoning with salt and pepper.
Pour the sweet mustard sauce over the sliced tongue. Serve warm.