Bring a large pot of salted water to a boil.

While the water is coming to a boil, put the garlic and ¼ cup olive oil in a small, heavy pot or skillet over medium to medium-high heat and cook the garlic until it begins to sizzle. Reduce the heat to low and cook until the garlic is light golden, soft, and fragrant, 5 to 7 minutes. Pour the oil and garlic into a bowl so it can cool quickly.

When the water reaches a rolling boil, add the kale leaves and cook until they are tender but not mushy, about 5 minutes. Use tongs or a slotted spoon to transfer the kale to a blender. It’s fine if they are still wet.

Add the pasta to the still-boiling water and cook until al dente according to the package instructions. With a ladle or measuring cup, scoop out about 1 cup of the pasta water and set it aside, then drain the noodles.

Process the kale in the blender with the oil and garlic, adding just a bit of the pasta water to help the process and make a nice, thick puree. Season with salt and pepper.

Transfer the drained pasta back to the pot and pour in the kale puree. Add half the Parmigiano- Reggiano cheese and toss well. Add a touch more pasta water and toss until the pasta noodles are well coated with the bright green, creamy-textured sauce. Serve right away with a big drizzle of olive oil and the rest of the cheese.