Cook kale leaves in a large pot of boiling salted water until bright green and wilted, about 30 seconds. Transfer to a rimmed baking sheet covered with a tea towel to dry.
Blend nuts (*if using walnuts lightly toast on low heat until fragrant first) in a food processor until crumbled or smooth depending on your texture preference.
Add kale, basil, and 1 oz. Parmesan/nutritional yeast. Purée until smooth.
Slowly add oil, mix until desired ratio and add salt to taste.