Soak the peas overnight in cold water to cover. Drain well. Peel and finely chop the carrot. Wash and shred the leeks and shred the celery. Melt the butter or bacon fat in a saucepan and add the vegetables. Sauté gently for about 5 minutes or until the vegetables are tender but not brown. Add the split peas and cook for a further few moments. Then stir in the stock, add a seasoning of pepper and the bouquet garni.
Cover with a lid and simmer gently for about 1 hour, or until the split peas are quite soft.
Draw the pan off the heat and remove the bouquet garni. Pass the soup through a vegetable mill or purée in a blender. Return the soup to the pan. Pour the milk into a basin and sift the flour over the surface; whisk until smooth and add to the soup. Bring up to the boil, stirring all the time until the soup has thickened. Taste and correct seasoning if necessary.
Serve with dice of crisply fried bread or with Italian grissini (bread sticks).