How to Make It
Place the beans in a large pot. Add 2 quarts of water and the onion, carrot, garlic, bay leaves and the reserved fennel stalks and core. Bring to a boil, reduce the heat to very low, cover and simmer until the beans are tender, about 1 hour. Season the beans with salt and pepper during the last 10 minutes of cooking.
Drain the beans and discard all the cooked vegetables. Coarsely chop the fennel fronds. Transfer the beans to a large serving platter and, while still warm, add the dill, diced fennel bulb, fennel fronds and all but 1 tablespoon of the olive oil. Season with salt and pepper and toss gently to combine.
In a medium nonstick skillet, heat the remaining 1 tablespoon of olive oil. Season the salmon on both sides with salt and pepper, add the fish to the skillet and cook over moderate heat on 1 side until brown and crusty, about 3 minutes. Gently flip the salmon and cook on the other side until just cooked through, about 4 minutes. Transfer the salmon to a plate to cool slightly. Break the salmon into large flakes and toss gently with the beans. Serve the salad warm or at room temperature.