If using dried black-eyed peas, rinse them under cold water and remove any debris. Soak them in water for at least 4 hours or overnight for softer peas.
In a large pot, heat the olive oil over medium heat. Add the diced onion, garlic, bell pepper, and celery. Sauté for about 5-7 minutes until the vegetables are soft and the onion is translucent.
If using dried peas, drain and add them to the pot. Pour in the 4 cups of water, broth, smoked paprika, black pepper, salt, and bay leaf. Bring to a boil, then reduce the heat to low, cover the pot, and let it simmer for about 30-40 minutes or until the peas are tender.
After simmering, check the peas for tenderness. If needed, add a bit more broth or water to reach your desired consistency.
If using canned black-eyed peas, add them to the mixture along with the bay leaf. Let it simmer for an additional 5-10 minutes to heat through.
If desired, stir in cooked bacon or ham for added flavor. Adjust seasonings if necessary.
Remove the bay leaf before serving and enjoy your Southern black-eyed peas hot as a main dish or as a hearty side.