Bring a large pot of salted water to a boil.

Meanwhile, in a large skillet, heat half the oil over medium-high. Add half the squash in a single layer, season with salt and cook, undisturbed, until browned, 3 to 5 minutes. Remove cooked squash to a plate, add remaining half of oil to the pan and cook the second half of the squash in the same way.

When the water comes to a boil, add the pasta and cook according to package directions until al dente. Reserve 1 cup of the pasta water, then drain the pasta.

Return cooked squash to the pan. Reduce the heat to medium-low, add the butter and stir with the squash until the butter is golden, nutty smelling and foaming, 1 to 4 minutes. Turn off the heat, add the red-pepper flakes, and stir until fragrant, about 1 minute. Add kale to the pot, tossing gently until coated with butter and beginning to wilt.

Add the pasta, ½ cup pasta water and about ¾ of the TomaProvence to the squash mixture. Set over low heat and toss gently until the cheese is melted and pasta is coated with sauce. If the pasta looks dry, add more pasta water as needed. Remove from heat. Season to taste with more red-pepper flakes and salt.

Remove to a serving bowl, top with remaining TomaProvence and serve.