Place the smoked turkey in a large pot and pour in the broth or water. Bring to a boil, then reduce the heat, cover, and simmer for about 1 hour, or until the turkey is tender.
Remove the turkey from the pot, keeping all the cooking liquid. When cool enough to handle, remove and discard the skin and bones, then shred or dice the meat.
Add the green beans, shredded turkey, onion, and garlic to the pot. Stir in the seasoned salt and black pepper.
Return to a simmer and cook for 10 minutes. Add the potatoes and stir gently.
Cover and simmer for another 20 to 30 minutes, until the potatoes and green beans are tender to your preference. Taste and adjust the seasoning before serving.