Put the potatoes in a large pot and cover with cold water by 2 inches. Add 2 tablespoons salt, bring to a boil, and cook until the potatoes are fork tender, about 25 minutes. Drain well. While potatoes are cooking, combine the butter and buttermilk in a small saucepan and bring to a simmer.
Working in batches, pass the cooked potatoes through a food mill set over a pot (or just use a potato masher!). Stir the hot buttermilk mixture into the potatoes until they are smooth and creamy. Season generously with pepper and add more salt as needed. Stir in the green onions. Cover and keep warm over a simmering pot of water until ready to serve.