Add kale, basil, walnuts, garlic, lemon, salt, pepper and 1/4 cup of olive oil to a food processor. Pulse on high.
Scrape down the sides and blend again. Add additional olive oil until desired consistency is reached. You may need to stop and scrape down the sides a couple of times.
Transfer to a bowl, cover and place in the fridge until ready to use. This will last about 3 days in the fridge.