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1
In a large bowl, cover beans by at least 4 inches water and let soak overnight. The next day, drain, transfer beans to a large pot, and cover with at least 2 inches of fresh cold water. Add halved onion, garlic, 1 celery stalk, carrot, and 1 bay leaf to pot. Season with salt. Bring to a gentle simmer over medium-high heat, then lower heat to maintain gentle simmer. Cook until beans are fully tender, about 45 minutes. (Bean cooking time will vary depending on age and exact type of bean; taste every 5 minutes until done.) Set aside to cool.
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2
Meanwhile, combine salmon in a large saucepan with enough cold water to cover. Add 1 stalk celery, remaining 1 bay leaf, and lemon halves with their juice. Heat over medium heat until water registers 170u00b0F on an instant-read thermometer (or until water is at just below a bare simmer, if you don't have a thermometer), then adjust heat to maintain temperature. Cook until salmon is 115 to 120u00b0F in the center, about 20 minutes. (If you don't have a thermometer, salmon should flake easily when done.) Drain salmon, discard aromatics, and let cool in refrigerator.
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3
Using your fingers, flake salmon into large pieces. In a large bowl, whisk together remaining 4 tablespoons lemon juice, olive oil, shallot, and dill. Season with salt and pepper. Add cooled and drained beans, diced celery, diced fennel, and arugula and toss well. Add salmon, season with salt and pepper, and toss gently to combine. Serve right away.
