Heat the olive oil in a large stockpot over medium-high heat.
Add the onion, green onions, bell pepper, and celery. Cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Add the garlic and cook for an additional 30 seconds, stirring constantly.
Add the ham hocks or ham bones, black-eyed peas, chicken stock, bay leaves, Creole or Cajun seasoning, cayenne pepper, and cumin. Stir to combine.
Bring the soup to a boil. Reduce the heat to low, cover, and simmer for approximately 2 hours, stirring every 30 minutes, until the black-eyed peas are tender. Add additional chicken stock or water as needed to maintain the desired consistency.
Remove the ham hocks or ham bones and bay leaves. If using meaty ham hocks, remove any usable meat from the bones, chop or shred it, and return it to the soup. Discard the bones, skin, and excess fat.
Stir in the diced cooked ham. Season with salt to taste.
Simmer uncovered for an additional 5 minutes, or until the ham is heated through. Serve warm.
Notes
No soaking required: Dried black-eyed peas do not need to be soaked before cooking. Simply sort through them and rinse well.
Ham hocks or ham bones: Smoked ham hocks add rich, smoky flavor, but leftover ham bones work just as well. Remove any usable meat from the bones before discarding.
Adjust the cooking time: Simmer until the black-eyed peas are tender, approximately two hours. Older dried peas may take longer.
Adjust the consistency: Add more chicken stock or water if the soup becomes too thick. For a thicker broth, mash some of the cooked peas and stir them back into the soup.
Season to taste: Ham, chicken stock, and Creole seasoning can be salty. Taste the soup before adding additional salt.