Bring a pot of water to a boil. Add the kale and cook for 1 minute. Immediately drain and dunk into ice-cold water to halt the cooking. Drain and wring out any excess water.
In a food processor, combine the kale, spinach, garlic, cheese and almonds. Pulse to combine. While the machine is running, stream in the olive oil, adding a little more until you reach your desired consistency. Add salt and pepper to taste, and pulse to combine again.