This is one of my daughter's favorite soups, and once you try it, it'll be yours, too.
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In a large pot, cover the peas with 2 quarts cold water and soak overnight. If you need a faster method, simmer the peas gently for 2 minutes, and then soak for 1 hour. For best results, go with the overnight method.
Melt the butter in heavy large pot or Dutch oven over medium-high heat. Add the onion, celery, and carrots. Sauté until the vegetables begin to soften, about 8 minutes. Add the pork and marjoram and stir for 1 minute. Add the peas, the 4 cups of water, chicken broth, and bring to boil. Reduce heat to medium-low. Partially cover the pot and simmer the soup until the pork and vegetables are tender peas are falling apart, stirring often, about 45 minutes.
Pull out the bone, pull the meat off, and chop. Return to the pan and simmer for 15 minutes or until ready to serve.