To make cocktail sauce combine all ingredients in a bowl and mix until thoroughly combined, cover and refrigerate until ready to use.
In a large stock pot add water, carrots, celery, garlic cloves, Old Bay, and salt. Bring to a boil, cover and reduce heat to maintain a low boil. Cook for 15 minutes.
While broth cooks, prepare an ice bath by placing 4-5 cups of ice in a large bowl along with 4 to 5 cups of cool tap water.
Remove pot from heat and add shrimp. Cook shrimp, stirring occasionally for 4-5 minutes or until cooked through. The shrimp will be pink and curled.
Once the shrimp has cooked remove them with a large, slotted, spoon and immediately place in the prepared ice bath to stop cooking. Allow shrimp to sit in the bath for 2-3 minutes or until thoroughly chilled.
Remove the shrimp from the ice bath and place them in a bowl or on a serving platter. Cover and refrigerate shrimp until ready to serve. Serve with prepared cocktail sauce or your favorite store-bought sauce and lemon wedges.