Cook collard greens and kale in a large pot of boiling salted water until bright green and tender, about 45 seconds. Transfer to a bowl of ice water (this will stop the cooking and help lock in the color). Drain; squeeze out as much liquid as possible (to avoid a watery sauce).
Coarsely chop greens and place in a food processor. Add garlic, Parmesan, oil, peanuts, lemon zest, and lemon juice; process on low speed until a coarse but well-blended mixture forms (a little texture is part of the selling point). Season with salt and plenty of pepper.
Pesto can be made 1 day ahead. Cover with plastic wrap, pressing directly against surface, and chill.
