In a food processor, combine the kale leaves, basil leaves, and salt. Pulse 10 to 12 times, until the kale leaves are finely chopped. With the motor running, drizzle in the olive oil. Scrape down the sides of the processor. Add the almonds, garlic, lemon juice, and zest and process again, then add the cheese and pulse to combine.
Serve immediately or store in an airtight container in the refrigerator for up to 2 days. To serve, toss with your favorite pasta or use as a topping for grilled meats, fish, or vegetables.