Remove the arils from the pomegranate and set aside. Soak the pear halves, round-side-down, in 1-1/2 cups pomegranate juice for 15 minutes, or until the desired shade of red is achieved.
Meanwhile, in a small non-reactive saucepan over medium high heat, bring the honey and remaining 1/2 cup pomegranate juice to a boil. When the mixture comes to a boil, remove the pan from the heat, carefully pour the honey and juice into a heatproof container such as a large liquid measuring cup and set the container in an ice bath to cool.
In the bowl of a food processor fitted with the blade attachment, process the feta cheese and olive oil until the mixture is smooth; set aside.
Drain and dry the pear halves with a clean towel. Slice the pears lengthwise, leaving the neck intact by making 1/4-inch thick slices from the wide, blossom end, four-fifths of the way up toward the stem end.
To assemble, place a sliced pear on each of 24 salad plates and fan out the slices. Smear 1 tablespoon of the whipped feta on the plate behind each pear. Toss 1/2 ounce of frisée lettuce with 1 teaspoon of the pomegranate honey and place it behind the pear, on the whipped feta. Sprinkle the feta with chopped pistachios and about 1/2 teaspoon sumac. Scatter pomegranate arils on top of each pear half and drizzle the remaining pomegranate honey over each pear.