Place peas in a colander; rinse under running water. Put peas in a large stockpot; cover with cold water and allow to soak overnight. (If using split peas, there's no need to presoak.) Drain.
In a large pot, melt the butter and saute onion until softened, about 2 minutes. Add peas, salt, salt pork, water and savory. Bring to boil; cover and simmer for about 1 1/2 hours or until salt pork is tender. Remove pork; chop and return to soup.
Continue simmering soup until peas are tender, about 30 minutes longer. Remove 2 cups peas from soup and process in food processor; stir back into the soup. Adjust seasoning and serve.
Serves 6.