Using a vegetable peeler, remove a strip of the peel from around the center of each potato. Set aside.
Heat butter over medium-high heat in a large skillet until melted. Add potatoes, kosher salt and pepper and stir to coat coat potatoes. Cover skillet with lid and cook for 10 minutes. Every 3 minutes, hold the lid down on the skillet and swirl the skillet in a circular motion in order to move the potatoes around in the skillet.
After 10 minutes, turn the heat to high and continue cooking, swirling every 3 minutes, until potatoes are tender and golden brown, about 8-10 minutes. Add half the green onions to the skillet and swirl one additional time to combine. Cook for 1 minute.
Garnish with the remaining green onions when serving.