How to Make It
Make the beans: Put the beans in a medium bowl, cover with 4 inches of cold water, and soak overnight; drain and rinse. Heat a medium saucepan over high heat for 2 minutes. Pour in the olive oil, add the rosemary sprig and crumbled chile, and let them sizzle in the oil for 1 minute. Add the onion, fennel, garlic, thyme, and bay leaf and cook, stirring, until the onion is softened, 1 to 2 minutes.
Add the white beans and cook, stirring to coat the beans in the oil, for 2 minutes. Cover with water by 3 inches, raise the heat, and bring to a boil. Reduce the heat to low and press a paper towel over the beans to keep them under the surface. Simmer for 30 minutes, add the salt, and continue cooking until the beans are tender, 1 hour, adding water if necessary. Remove the beans from the heat, discard the paper towel, and allow them to cool in their liquid.
Make the cavolo nero: Prepare an ice water bath in a large bowl. Bring a large pot of heavily salted water to a boil over high heat. Working in batches, blanch the cavolo nero for 2 minutes, submerge in the ice water bath, drain, let cool, and squeeze out the excess water with your hands.
Heat a large pot or Dutch oven over medium heat for 2 minutes. Pour in 2 tablespoons of the olive oil, add the rosemary sprig and crumbled chile, and let them sizzle in the oil for 1 minute. Reduce the heat to medium-low, add the sliced onion, and season with ½ teaspoon of salt and the pepper. Cook for 2 minutes, then stir in the sliced garlic and continue to cook, stirring often with a wooden spoon, until the onion is soft and starts to brown, 5 to 7 minutes.
Add the cavolo nero and remaining 2 tablespoons olive oil, stirring to coat the greens with oil and onions. Season with ¼ teaspoon salt and cook slowly over low heat, stirring often, until the greens turn dark, almost black, and get slightly crispy on the edges, 30 minutes.
Remove and discard the rosemary and the chile.
Roast the tomatoes: Preheat the oven to 450°F. Place the tomatoes on a small baking sheet, drizzle with the olive oil, and season with the salt and pepper. Roast until the tomatoes begin to break apart and char, 30 minutes.
Make the gremolata: Chop the parsley, lemon zest, and garlic together until very finely minced; set aside.
Bake the eggs: Raise the oven temperature to 500°F. Place the beans, along with 1 cup of their cooking liquid, in a large (at least 12-inch) cast-iron skillet. Place the cavolo nero on top of the beans, then cover with the tomatoes and the olives. Roast until the beans and vegetables are thoroughly heated, 8 to 10 minutes. Carefully remove the skillet from the oven, crack in the eggs, and season with salt and pepper to taste. Return to the oven and bake until the eggs are just set, 4 to 5 minutes. Remove from the oven, divide among shallow bowls, and sprinkle with the gremolata.