Bring a large pot of generously salted water to a rolling boil. Prepare a large bowl of ice water and set it beside the stove. Add the black kale leaves and blanch for 1–2 minutes, just until tender and bright green. Using a slotted spoon, transfer immediately to the ice bath.
In the same pot, blanch the basil for 20–30 seconds, just until vibrant. Transfer directly to the ice bath. Once cooled, drain the greens and squeeze out as much excess water as possible using your hands or a clean kitchen towel. Set aside.
Bring the same pot of water back to a boil if needed. Cook the pasta until al dente or according to the box instructions. Reserve ½ cup of pasta water before draining.
While the pasta cooks, make the pesto. In a food processor, combine the blanched kale, basil, pine nuts, garlic, lemon zest, lemon juice, Parmesan, ½ cup of the olive oil, salt, and pepper. Blend until mostly smooth. With the processor running, slowly drizzle in the remaining ¼ cup olive oil until emulsified, glossy, and vibrant. Taste and adjust seasoning as necessary.
In a small skillet over low to medium heat, melt the butter. Add the breadcrumbs, along with a pinch of salt and pepper. Toast, stirring often, until golden and crisp, 3-4 minutes. Remove from heat.
Return the drained pasta to the pot over low heat. Add the pesto and toss to coat, adding splashes of reserved pasta water as needed to loosen the sauce and help it cling to every ridge.
Transfer to a serving bowl. Finish with the toasted breadcrumbs, fresh basil, extra lemon zest and juice, and a final crack of black pepper. Serve and enjoy!