Combine first 9 ingredients in a Dutch oven; bring to a boil. Reduce heat; simmer 30 minutes. Return mixture to a boil; add shrimp. Cook 3 minutes or until done. Drain shrimp in a colander over a medium bowl, reserving cooking liquid. Rinse shrimp under cold water; drain well. Set aside. Discard celery stalks, garlic, and bay leaves from cooking liquid; set cooking liquid aside. Let cool completely.
Add shrimp to cooled cooking liquid, and cover and marinate in refrigerator 24 hours.
Combine chopped celery and next 7 ingredients (celery through black pepper) in a small bowl; stir well. Cover and chill 24 hours.
Drain shrimp; discard liquid. Combine shrimp and 1/2 cup remoulade in a bowl; stir well. Arrange 1/2 cup watercress on each of 4 plates; top each with 6 shrimp and 2 tablespoons remoulade.