Prepare fresh pomegranate juice, if necessary.* In a small bowl, mix 1/2 oz. pomegranate juice, 1 teaspoon champagne vinegar and 1 teaspoon minced shallot; season with salt and pepper. While mixing, add 4 tablespoons of extra virgin olive oil.
Peel, deseed and dice avocado into 1/4-inch cubes. Toss with the juice of half a lemon and reserve.
In a mixing bowl, whisk heavy cream until stiff peaks form. Add 1/2 teaspoon of lemon juice and 1 teaspoon of horseradish; salt and pepper to taste.
Prepare fresh pomegranate arils, if necessary.** In a medium saucepot, add water, onion, carrot and celery (cut into large pieces), juice of half a lemon, fresh thyme, bay leaf, and 3 tablespoons of salt. Bring the pot to a boil and let simmer for 5 minutes. Add shrimp and remove the pot from heat. Allow the shrimp to poach in the liquid for 3 minutes, then remove, peel and devein.
On a plate, toss diced avocado with a teaspoon of vinaigrette, salt and pepper. Arrange 1 teaspoon of avocado on plate and place poached shrimp on top. Dress a handful of baby mache with 1 teaspoon of the POM Vinaigrette and place on top of the shrimp, then season with salt and pepper. Sprinkle fresh arils and add a dollop of the horseradish cream. Finish with a drizzle of 1/2 teaspoon of vinaigrette around the plate.
*To prepare fresh pomegranate juice, cut 2–3 large POM Wonderful Pomegranates in half and juice them with a citrus reamer or juicer. Pour the mixture through a cheesecloth-lined strainer or sieve. Set the juice aside.
**To prepare fresh arils, score 1 large POM Wonderful Pomegranate and place in a bowl of water. Break open the pomegranate under water to free the arils (seed sacs). The arils will sink to the bottom of the bowl and the membrane will float to the top. Sieve and put the arils in a separate bowl. Reserve 1/2 cup of the arils from fruit and set aside. (Refrigerate or freeze remaining arils for another.