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 them 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.) 

Discard the onion, carrots, kombu, and bay leaves and strain the beans, reserving all of the cooking liquid. 

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 ½ 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. 

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.