Fill a large saucepan halfway with water and bring to a boil over high heat. Meanwhile, prepare a medium mixing bowl filled with 2 cups of ice and 6 cups of cold water. This bowl will be used to shock your arugula after blanching.
Add washed arugula in two batches to the boiling water. Submerge in water for about 20 seconds and remove with a slotted spoon. Transfer the hot arugula to the ice water bath and submerge. Use your hands to squeeze out the water from the arugula and set aside until needed.
In a food processor, add garlic cloves, walnuts, and parmesan, and blend for 10–20 seconds. You want it slightly chunky. Add the blanched arugula. Blend for 10 seconds or so. Add the spinach and pulse until the leaves are incorporated. Finally, pour in the olive oil, salt, black pepper, and lemon. Blend until fully incorporated.