Heat a large saucepan filled with water over medium high heat. Prepare an ice bath by filling a large bowl of water with ice.
Place walnuts in a small skillet and toast over medium heat until edges are slightly browned and the nuts release their aroma. Set to the side to cool slightly.
Remove the kale leaves from stems and give them a rough chop. Discard or compost stems. Set the chopped leaves aside while gathering and measuring the remaining ingredients as the water heats to a boil.
Once the water boils, add the chopped kale leaves and blanch for one minute. While the leaves blanch, fill the ice bath bowl with water. Promptly remove the kale leaves from the pot and immediately place into the ice bath. The ice bath helps to slow the cooking process, keeping the leaves green.
Drain the blanched kale leaves and gently squeeze out any remaining water. Place the blanched kale leaves on a clean kitchen towel to blot off any extra water. Then, place the leaves in the food processor fitted with the metal chopping blade.
Add the toasted walnuts, garlic cloves, lemon zest, and season with kosher salt and ground black pepper. Pulse the initial ingredients in the food processor to roughly chop and combine.
Next, with the food processor running, slowly add the olive oil in a slow and steady stream. Process the pesto until smooth.
Spoon pesto into a storage container and stir in the parmesan cheese. Taste and adjust seasoning with a pinch of kosher salt, if desired.