Rinse the potatoes thoroughly and place them in a large pot. Do not peel.
Add enough water to fully cover the potatoes, then add the salt. The water should taste very salty, similar to brine.
Bring the pot to a boil over high heat and cook uncovered until the potatoes are fork-tender, about 20–25 minutes.
Drain the potatoes completely and let them rest in the hot pot for 1–2 minutes so excess moisture evaporates. Do not rinse.
Split the potatoes open and serve immediately with melted butter poured over the top.