Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 15 minutes. Drain potatoes and save about 1/2 cup cooking water in the pot.
Add 2 or 3 potatoes pieces back into the pot with the cooking water and mash them to thicken the sauce a bit. Add butter and stir until melted. Stir in green onions. Return hot potatoes to the pot and stir gently until coated in the sauce.
Let sit until potatoes soak up the butter sauce, 5 to 7 minutes. Season with salt and pepper if desired. Serve hot.