Put potatoes in a large pot, add 1 teaspoon salt, cover with water and bring to a boil. Turn down heat and simmer, uncovered, for about 15 minutes, or until potatoes are tender. Drain and when cool, cut potatoes in half.
In a large skillet, heat olive oil and butter, then add potatoes and cook until golden brown, about 5-7 minutes. Add onions and garlic and cook until onions are softened and slightly golden, stirring occasionally to prevent potatoes from sticking to the pot. Add the greens, cover and cook until greens are tender, about 10 minutes. Season with salt and pepper to taste.