Rinse and sort peas to remove debris and dirt. Then, soak peas using whatever method you prefer. See Notes below.
Heat a large pot over medium-high heat. Once hot, add the olive oil and add the diced onion, green pepper, and celery to the pot and cook for 4-6 minutes until the vegetables are almost translucent. Then, add 1 tsp of salt, minced garlic, celery seed, smoked paprika, black pepper, and sugar, and cook for an additional 1 minute.
Then, add the chicken broth, followed by the black-eyed peas, bay leaves, thyme, and an additional 1 tsp of salt to the pot. Stir until well combined. Then, and the smoked turkey leg.
Bring the soup to a boil and then reduce to a simmer and cover. Let the peas simmer for about 30-40 minutes or until the black-eyed peas are tender, stirring occasionally. When the peas are tender, take out the smoked turkey leg, shred it, and add it back to the peas. Let the soup simmer for an additional 5 minutes. Then, give the peas a taste and adjust the seasoning as needed — I typically add a bit more salt.
When you are ready to serve, add green onion to each bowl as garnish and serve with corn bread.