Remove and discard ham bone, leaving bits of ham that would have cooked into the black eyed peas in the peas. If using bacon or salt pork, remove and discard. Salt and pepper to taste.
Add peas back to the stock pot and return to stove over medium-low heat. Add enough water to the stock pot to cover the black eyed peas, plus about 2 inches. Add in ham bone, bacon or salt pork. Bring black eyed peas to a simmer and continue to keep at a low simmer, adding water and stirring occasionally as needed, until the black eyed peas are fork tender, about two hours.
Pour rinsed black eyed peas into a large, heavy-bottomed stock pot and soak overnight. Pour black eyed peas through a colander again to remove them from the water they soaked in overnight.
Rinse black eyed peas in a colander, discarding any peas that are discolored or any small pebbles that may be in the dried peas.