Add the kale and half of the olive oil to a food processor. Pulse to break down the kale as much as possible, scraping down the sides as needed.
Add the remaining ingredients and blend until they are completely broken down. Add more olive oil as necessary and scrape the sides several times. It took me about 10 cycles of blending and scraping to get mine to a consistency I liked. I added about a cup of olive oil total.
Taste and adjust the seasonings before serving.