Place the peeled potato chunks into a large pot and cover with cold salted water. Bring to a boil and cook until fork-tender, about 18–20 minutes.
While the potatoes cook, combine the milk and sliced green onions in a small saucepan. Warm over low heat for 4–5 minutes until steaming but not boiling.
Drain the potatoes well and return them to the warm pot. Heat over low heat for 1 minute to remove any remaining moisture.
Add the butter to the hot potatoes and mash until mostly smooth. The butter should melt completely into the potatoes.
Slowly pour the warm milk and scallion mixture into the potatoes while gently stirring. Mix until creamy and fluffy without overworking the potatoes.
Season with salt and black pepper. Taste and adjust the seasoning if needed.
Transfer the champ to a serving bowl or plates. Make a small well in the center and add an extra pat of butter.
Garnish with chopped chives or extra sliced green onions and serve immediately while hot.