In a large pot, add the potatoes and fill with water until it reaches halfway up the potatoes. Bring the water to a boil, then reduce to a simmer and cook until the potatoes are tender, about 40 minutes. Drain the water, but leave the potatoes in the pot. Cover and let rest 5 minutes.
In a large skillet, melt butter over medium heat. Add the chopped kale and saute, stirring often, until wilted, about 5 minutes.
In a medium saucepan, simmer milk and chopped green onions over medium low heat, about 5 minutes. Season with salt and pepper. Remove pan from heat, stir in wilted kale, and cover.
Peel the potatoes and place in a large bowl. Add the milk mixture and mash until only a few small pieces remain. Season with salt and pepper to taste.
Serve warm with a pat of butter on top of each bowl.