Method:
Preheat oven to 350°F. Spread pistachios on a baking sheet and bake until browned and fragrant, stirring halfway through, 7 to 8 minutes. Transfer pistachios to a plate to cool.
Peel pears, cut them into quarters and remove cores and stems. Place pears in a large saucepan with pear juice and water. Bring liquid to a boil, reduce heat to a simmer, cover and cook until pears are tender when pierced with a fork, about 20 minutes.
Process 1 cup of toasted pistachios (reserve remaining nuts for garnish) in a blender until finely ground. Add cream and just enough pear cooking liquid to pistachios to achieve a smooth consistency. Transfer pistachio cream to a large bowl. Puree pears with their cooking liquid in the same blender, in batches, until smooth and creamy. Add pureed pears to bowl with pistachio cream. Stir in maple syrup and ground cardamom to taste.
Cool soup and chill completely, at least four hours or up to overnight. Serve soup garnished with pomegranate seeds and coarsely chopped toasted pistachios.