Combine water and 2 teaspoons salt in a large saucepan. Cover and bring to a boil. Add shrimp; cook, uncovered, 3 minutes. (Do not boil.) Drain; rinse in cold water. Peel and devein shrimp; set aside 4 shrimp. Chop remaining shrimp.
Combine chopped shrimp, lettuce, celery, cucumber, chopped parsley, onion, mayonnaise, 1/4 teaspoon salt, and pepper in a medium mixing bowl; stir well to blend. Cover with plastic wrap, and chill.
To serve, spread partially split hard rolls with softened butter. Fill each roll with one-fourth of chilled shrimp mixture. Transfer shrimp rolls to a serving platter, and garnish with reserved shrimp and parsley sprigs.