Put the water in a large stockpot, add the salt, and bring to a boil. Add the peanuts and simmer for 1 to 2 hours, testing a peanut occasionally, until the shells tear open with ease and the peanuts inside are completely tender (even a little mushy).
Drain and serve warm. Uneaten peanuts can be stored in a tightly covered container in the refrigerator for up to 2 days. Heat cold peanuts to hand-hot in the microwave before serving.
Note: To make this recipe, you must have green peanuts--uncooked, fresh peanuts, which are still tender and not dried or crunchy. Outside the Southern US, green peanuts can sometimes be purchased at specialty or gourmet stores, or mail-ordered. Don't try this with dried or cooked peanuts.