Heat the oil in a Dutch oven over medium heat until it begins to shimmer. Stir in the onions and cook until softened and translucent, about 5 minutes.

Stir in the garlic, thyme, and red pepper flakes and cook until fragrant. Add the beans and broth, bring the mixture to a simmer, and cook until the sauce has thickened slightly, about 10 minutes.

Stir in the kale, cover the pot, and cook until the leaves are tender, about 10 to 12 minutes, stirring occasionally to ensure even cooking.

Remove the pot from the heat and mash a portion of the beans against the side of the pot with a wooden spoon to create a creamier consistency. Season with salt and pepper to taste.

While the sauce is simmering, bring 4 quarts of water to a boil in a separate large pot. Add the pasta and salt and cook until al dente. Reserve 1/2 cup of the cooking water before draining the pasta.

Return the drained pasta to its pot and stir in the kale-bean mixture, half of the Parmesan, and the remaining oil. Toss to combine, adding the reserved cooking water as needed to adjust the sauce consistency.

Season with additional salt and pepper, then serve in warm bowls topped with the remaining Parmesan.