Bring a large pot of salted water to a boil. Cook the 12 ounces cavatappi to al dente according to package directions. Before draining the pasta, reserve 1 cup of the cooking water.
Meanwhile, pulse the 3 cups kale, 1 cup fresh basil, 2 Tablespoons olive oil, ¼ cup walnuts, 2 cloves garlic, lemon zest & juice and ½ teaspoon salt in a food processor until smooth. Set aside.
Heat the 2 Tablespoons olive oil in a large skillet over medium-heat. Add the 1 shallot and 2 cloves garlic and cook, stirring occasionally, until just softened, about 2-3 minutes.
Add the 4 ounces goat cheese, pasta and ½ cup of the reserved pasta cooking water to the shallot/garlic mixture. Cook, over medium heat, stirring gently, until the cheese coats the pasta, adding additional cooking water if needed to loosen the sauce.
Add the pesto and stir gently to combine.
Serve garnished with additional chopped basil, walnuts and goat cheese, if desired.