Soak the beans in 3 cups cold water for 12 hours or overnight. Drain and transfer into a large saucepan with the bay leaves. Pour in cold water so the beans are covered by 2 inches and bring to a simmer over medium heat. Cover and cook for 45 minutes to an hour (or according to package instructions), until the beans are tender but not mushy. Check the water level from time to time, and add more if it runs a little low. Thirty minutes into the cooking, add 1 1/2 teaspoons of the salt. (The beans can be prepared up to a day ahead).
While the beans are cooking, combine the walnuts, arugula (reserve a few leaves for garnish if desired), oil, lemon juice, shallot, and the remaining 1/2 teaspoon salt in a food processor or in a mortar. Process or grind with a pestle until the mixture forms a paste-like dressing. (The dressing can be prepared up to a day ahead. It can also be used in potato or chicken salad, or as a sandwich spread).
Drain the beans and let cool for a minute. Pour the dressing into a salad bowl, add the beans, and toss gently to coat. Garnish with the reserved arugula and serve while still warm. The leftovers are just as good the next day, cold or gently reheated.