In a 4-qt. saucepan, combine the beans with 6 cups water and bring to a boil. Reduce the heat to maintain a simmer and cook the beans until just tender, about 20 minutes. Drain the beans and reserve 2 cups of their cooking liquid.
In a large saucepan, heat 2 tablespoons olive oil over medium. Add the fennel seeds and onion and cook, stirring, until soft, about 10 minutes. Stir in the beans and 6 cups fresh water, season with salt and pepper, and bring to a boil. Reduce the heat to maintain a simmer and cook until the beans are falling apart, about 25 minutes. Using an immersion blender or working in batches with a standard blender, purée the soup until smooth. Stir in the reserved cooking liquid, season with salt and pepper, and keep warm.
Meanwhile, in a pot of boiling salted water, cook the broccoli rabe until crisp-tender and bright green, about 2 minutes. Drain the broccoli rabe and transfer to a bowl.
In a medium skillet, heat the remaining 2 tablespoons olive oil over medium-high. Add the chile flakes and garlic and cook for 2 minutes. Stir in the broccoli rabe, season with salt and pepper, and cook until warmed through, about 2 minutes. Divide the soup among bowls and top each with some of the broccoli rabe and a drizzle of more olive oil before serving.