In a blender or food processor, combine the kale, basil, parmesan, olive oil, and a pinch of salt and crushed red pepper. Pulse until chunky smooth. Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water. Drain the pasta. Meanwhile, heat the butter, walnuts, thyme, lemon zest, and a pinch of salt in a large skillet. Cook 5 minutes, stirring occasionally, until the butter is browned and the walnuts are toasted. Remove the nuts from the skillet to a plate.Add the garlic to the skillet, cooking 1 minute, until fragrant. Drop the pasta into the skillet. Add the kale pesto, lemon juice, and a pinch of pepper. Toss to combine. Thin the pasta as desired with the reserved pasta cooking water.Break the burrata into the bottom of each individual serving bowl. Spoon the pasta over the cheese. Top with the buttery walnuts. Enjoy!