Bring a large pot of salted water to a boil for the pasta. Once boiling, add the pasta and cook according to package directions until al dente. Drain in a colander and let cool for 5 minutes.

While the pasta is cooking, prepare the pesto. Pull the kale leaves from the woody stems, and roughly chop into thin strips. Place the kale in a colander and rinse with cool water. Gently shake to remove excess water.

Add the chopped and washed kale to a food processor along with the olive oil, 1/4 cup lemon juice, garlic, walnuts, Parmesan, salt, and pepper. Purée the mixture until smooth and bright green. Add more oil, 1 tablespoon at a time, if needed to achieve a thick, smooth sauce. Taste the pesto and adjust the salt, pepper, or lemon juice to your liking.

Once the pasta is drained and cooled to the point where it is no longer steaming, transfer it to a large bowl. Add about half of the pesto and stir until the pasta is evenly coated.

Dice the mozzarella into small cubes, then add it to the pasta along with about 1 Tbsp of the lemon zest. Stir to combine with the pesto pasta. Add more pesto, 1/4 cup at a time, until everything is coated in a thick layer. Top with more freshly cracked pepper and serve, or refrigerate until ready to eat.