In a large heavy pot (like a Dutch oven), heat 2 to 3 inches of oil to 350 degrees F.
Thoroughly wash the kale and remove the stems. Tear the leaves up into large bite-size pieces and dry them, either in a salad spinner or on paper towels.
Drop 5 to7 leaves in the hot oil at a time and fry until the kale is crisp and almost transparent, 60 to 90 seconds. Drain on a wire rack set over paper towels and season with kosher salt while hot.
Fry the cilantro leaves for a couple of seconds and drain on the same wire rack. Season with a bit more salt. Serve it as a snack or side dish.