Remove the central tough stem from the kale leaves and discard. Coarsely chop the leaves and add them to the bowl of a food processor fitted with a blade.
Add the pepper, garlic, salt, capers and juice, and cheese.
Pulse until it's ground to a coarse paste. Add the olive oil while pulsing.
Pour into a jar, top it with a little slick of olive oil and cover. Keep in the refrigerator for up to one week.