In a large stockpot over high heat, combine the water and turkey necks and bring to a rolling boil. Turn the heat to a low boil, cover and cook for 2 hours.
After the 2 hours, add more water if needed just to cover the necks, then add the onion, garlic and bouillion powder and stir to combine. Taste for seasoning and if you think there needs to be a little salt, add now but I wouldn't go overboard since the liquid will already have some good flavor for sure.
Add the potatoes and string beans, re-cover, and keep cooking on that low boil until the potatoes get tender and the beens are nice and soft. This takes about 45 minutes. Add the pepper and stir to combine. Taste for seasoning and adjust if needed. Take off heat but leave covered.
Pull the turkey necks from the broth and set them aside just until they are cool enough to handle. Pull the meat from the necks, discarding the skin and bones, and add the meat back to the broth. If you are using ham hocks, you can simply break them up with a cooking spoon in the pot, or remove them, pull the meat, and add it back into the broth, discard the bones and skin.
Serve the beans and potatoes in bowls along with some of the broth and meat.