If using dried black-eyed peas, rinse them under cold water and soak them in water for at least 4 hours or overnight. Drain and set aside.
In a large pot, heat olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes until translucent.
Add the minced garlic, diced carrot, and diced celery to the pot. Cook for another 5 minutes until the vegetables are tender.
Stir in the soaked black-eyed peas (or canned peas if using), then add water, thyme, smoked paprika, bay leaf, salt, and pepper. If using bacon or ham, add it now too.
Bring the mixture to a boil, then reduce the heat to low and let it simmer uncovered for about 30 minutes. Stir occasionally until the peas are tender.
Remove the bay leaf and adjust salt and pepper to taste.
Serve hot, garnished with fresh herbs if desired.