In a large pot that will comfortably fit the potatoes, add enough water to cover the potatoes and add ½ cup of sea salt.
Boil the potatoes until just fork tender.
Remove potatoes from water and set aside. (They can be cooled and refrigerated for later grilling at this point). Some of the salt will dry onto the skin of the potato and you might notice it has a white cast. This will add extra flavor to the skin.
Let potatoes cool enough to handle and then slice in half, lengthwise.
Just before grilling, brush the flesh side of the potato with melted butter and place on the grill flesh side down. Depending on the heat of your grill, grill long enough to get grill marks and then flip over to grill the skin side. Approximately 2-3 minutes on each side.
Remove from grill, plate, and sprinkle the sliced green onions over all the potatoes.
Serve with sour cream on the side if desired.