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Combine the beans in a large pot with enough water to cover by 2 inches. Add the onion, carrots, kombu, and bay leaves, turn the heat to medium-high, and bring the beans to a boil. Let then boil for 5 minutes, then reduce the heat so the beans are at a bare simmer, cover, and cook until the beans are very tender, about 1 hour. (Alternatively, you can cook the beans, water, and aromatic vegetables in a stovetop or electric pressure cooker: Bring to high pressure and cook for 17 minutes if using a stovetop model or 20 minutes for electric. Let the pressure release naturally, then open.)
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Discard the onion, carrots, kombu, and bay leaves and strain the beans, reserving all of the cooking liquid.
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In a deep skillet, heat the olive oil over medium heat until it shimmers. Stir in the broccoli rabe and sauté until very tender, about 8 minutes. Stir in the garlic and cook until it starts to soften, about 2 minutes. Stir in the drained beans, 1 1/2 cups of the reserved cooking liquid, and the salt. Cook just until the beans are hot and the flavors have melded, 2 to 3 minutes. Stir in the pepper, taste, and add more salt if needed.
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Divide the toast among shallow serving bowls. Drizzle with the chile oil, if desired, and spoon the bean mixture and broth on top. Finish with the Parm and serve hot.