Tuscan kale, also known as cavolo nero, dinosaur kale, and lacinato kale, is sweeter and more tender than regular kale, which can be used instead but may require more cooking time.
Combine oil, onion, garlic, and 1/4 teaspoon salt in a large saute pan; cook over medium heat, stirring occasionally, until onion is lightly browned, about 5 minutes. Reduce heat to medium-low; cook until onion is soft, about 10 minutes.
Add vinegar to pan, and raise heat to medium-high. Add kale, 1/4 cup water, and remaining 1/2 teaspoon salt; cook, stirring, until kale begins to soften, about 3 minutes. As the pan becomes dry, add another 1/4 cup water, and cook until the kale is tender, about 3 minutes more. Serve immediately.