To prepare shrimp, combine the first 6 ingredients in a large saucepan; bring to a boil. Add shrimp; cook 2 minutes. Drain; rinse with cold water until cool. Drain; discard bay leaf.
To prepare sauce, combine green onions and next 9 ingredients (through 1/8 teaspoon salt) in a large bowl; add shrimp, tossing to coat. Cover; chill 20 minutes. Arrange 1 cup arugula on each of 4 salad plates; top each serving with 1/2 cup shrimp mixture.