Put the heart, tongue, skirt and oxtail in a pot large enough to hold them all comfortably. Fill with water, up to the level of the meat. Bring to a simmer and cook gently for 1½ hours. Periodically skim off the scum that rises.
Add the whole leeks, carrots, onions and parsnips, the tomatoes, celery, garlic, bouquet garni and peppercorns. Simmer for another hour, or until the skirt is tender. Remove the skirt from the pot. Simmer the remaining meat for another hour or so, removing each cut as it becomes completely tender – the oxtail will be ready first, then the tongue and heart.
Cut the oxtail off the bone. Remove the skin from the tongue. Cut all the meat from the tail, tongue, heart and skirt into 2-3cm chunks.
Remove all the veg and herbs from pot and discard them. Strain the stock (or ‘bouillon’) through muslin or a fine cloth into a wide, shallow saucepan. Bring to the boil, then keep boiling until the bouillon has reduced by at least one-third and is well flavoured.
Drain the pearl barley and add it to the reduced bouillon. Simmer for 10 minutes or until the barley is about half-cooked. Add the fresh sliced carrots, parsnips and celeriac, simmer for another 5 minutes, then add the leeks. Simmer for another 5 minutes or so, or until the leeks are almost tender, then add the cubed, cooked meat. Simmer for a few more minutes, until all the meat is piping hot. Season to taste with salt and pepper, then ladle into deep dishes or bowls, and serve.
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