Place the walnuts in a large pan (12-inch) with a lid, and turn the heat up to medium. Toast the walnuts, stirring occasionally, until just fragrant, about 3 minutes, taking care not to burn them. Add 1 tablespoon of the olive oil, season with salt and pepper, give a stir for 1 minute and transfer to a small bowl. Wipe out the pan to make sure there aren’t any walnut pieces remaining.

Bring a large pot of well-salted water to a boil for the pasta. Add the remaining olive oil and the garlic to the pan and cook over low, stirring occasionally, until fragrant, about 2 minutes. Add the red-pepper flakes, stir and cook until fragrant, about 30 seconds to 1 minute. Increase heat to medium, add the kale to the pan in batches, using tongs to turn and wilt the kale in the garlicky oil, and season with salt and pepper.

Once all the kale is in the pan, reduce the heat to medium-low and cover. Add the spaghetti to the pot of water at this point and cook until al dente, according to package directions. As the spaghetti cooks, add a couple of ladles of the starchy pasta water to the kale to help it wilt down.

Squeeze half of the lemon over the kale and toss. Taste the kale and add more lemon juice and salt and pepper to taste, being mindful that you’ll also be adding the salty pecorino or Parmesan.

Once the pasta is cooked, set the pot next to the pan and use tongs to transfer the spaghetti to the kale. Ladle in more of the starchy water if the pan seems dry, and toss well until the pasta is glossy and silky. Add half of the walnuts and some grated cheese (about 3 tablespoons). Taste and drizzle with a little more olive oil and another squeeze of lemon, if you like. Remove from the heat, shower with more grated cheese, top with the remaining walnuts and serve.