Place whole potatoes and 2 teaspoons salt in a large pot and add water to cover. Bring to a boil. Reduce heat to medium high; cook until tender, 30 to 35 minutes. Drain, return to pot, and keep warm.
While potatoes are cooking, heat olive oil and 1 teaspoon butter in a medium skillet over medium heat. Add onions and sugar, 1/2 teaspoon salt, and 1/8 teaspoon pepper; saute, stirring occasionally, until caramelized, about 20 minutes. Set aside.
Meanwhile, remove stems from greens. Roughly chop a quarter of the greens; set aside. Place remaining greens in a serving bowl.
While potatoes are still hot, roughly mash using a large fork or a whisk. Add hot milk, remaining butter, 1/2 teaspoon salt, and 1/8 teaspoon pepper; mash to combine. Stir in half the onions and the chopped greens. Place potatoes over greens in bowl; top with remaining onions. Serve hot.