In a Dutch oven or large stockpot, add the potatoes and 2 tablespoons of salt. Add cold water to cover potatoes by 1 inch. Over medium-high heat, bring to boil and partially cover pot. Cook until potatoes are tender when pierced with a paring knife, stirring once or twice, about 10 to 15 minutes. Drain well, tossing in colander to remove excess water.
Wipe pot dry. Over medium-high heat, melt butter. Add kale and onion and cook until softened, about 5 minutes, stirring often.
Return potatoes to pot and mash to a uniform consistency. Slowly stir in ¾ cup hot milk. Add more milk, 1 tablespoon at a time, to adjust the consistency as desired. Season to taste with salt and pepper.
