Taste and texture will depend on the kind of beans used.
Soak beans overnight in cold water to cover. (Drain or not, as you prefer.) Add cold water to cover, celery leaves, and onion, bring to a boil, reduce heat, and simmer, uncovered, until beans are tender 30 minutes to 1 hour, depending on the variety. As beans cook, fry salt pork in small skillet until crisp. When beans are done, add salt pork and potatoes. Simmer, partially covered, 15 minutes or until potatoes are tender, adding water if necessary. Stir in milk, season with salt and pepper, and heat thoroughly. Garnish with chopped parsley.