Rinse the stomach thoroughly and soak overnight in cold salted water.
Rinse the liver, heart, and tongue. In a large pot of boiling, salted water, cook these parts over medium heat for 2 hours. Remove and mince. Remove any gristle or skin and discard.
In a large bowl, combine the minced liver, heart, tongue, suet, onions, and toasted oats. Season with salt, pepper, and dried herbs. Moisten with some of the cooking water so the mixture binds. Remove the stomach from the cold salted water and fill 2/3 with the mixture. Sew or tie the stomach closed. Use a turning fork to pierce the stomach several times. This will prevent the haggis from bursting.
In a large pot of boiling water, gently place the filled stomach, being careful not to splash. Cook over high heat for 3 hours.
Serve with mashed potato, if you serve it at all.