Cook potatoes in enough salted water to cover, until tender, about 15 minutes. Drain thoroughly. When cool enough to handle, cut potatoes in half. Meanwhile, wash greens in cold water and discard tough stems.

In a large, heavy skillet, heat oil and butter over medium heat. When foam subsides, add potatoes, cut-side down, and cook until golden, about 5 minutes. Use a spatula to loosen potatoes from skillet. Add garlic and cook, stirring, for a minute or two until golden, not brown. Add greens, cover and cook until wilted, about 3 minutes. Season to taste with salt and pepper.