Tear kale into large pieces. Bring a large pot of salted water to a boil and cook the kale for about 5 minutes, until tender. Pour into a colander and press with the back of a large spoon to remove excess liquid.
Meanwhile, heat the oil and butter in a large, heavy skillet (cast iron, if you have it) set over medium-high heat. Add the walnuts and cook, stirring, until golden and fragrant. Stir in the garlic. Remove the walnuts and set aside, and add the kale to the pan. Season with salt and pepper and cook until heated through.
Add the walnuts back to the pan and serve immediately.