Sort and rinse the green peanuts under cool running water to remove dirt; drain well.
Combine the water and kosher salt in a large pot and bring to a boil over high heat.
Add them, ensuring they’re submerged; place a heatproof plate or small lid on top as a weight if they float. Return to a gentle boil, then reduce to maintain a steady simmer.
Simmer 90–180 minutes, partially covered, until the shells yield easily between your fingers and the kernels are tender and pleasantly salty; begin tasting after 60 minutes and continue every 20–30 minutes.
Turn off the heat and let stand 20–30 minutes in the hot liquid to absorb more seasoning; for very salty peanuts, extend the soak to 1–2 hours.
Drain well and serve warm; or cool in the liquid, transfer to containers, and refrigerate up to 1 week or freeze for longer storage.