If using mascarpone cheese, omit this step. For yogurt cheese, line a strainer, sieve, or small colander with 3 layers of 100% cotton cheesecloth or a clean paper coffee filter. Suspend lined strainer over a bowl. Spoon yogurt into strainer. Cover with plastic wrap. Refrigerate at least 24 hours or up to 48 hours.
In a medium saucepan combine pomegranate juice and granulated sugar. Bring to boiling; reduce heat. Boil gently, uncovered, for 20 to 25 minutes or until reduced by half. Transfer to a bowl; cover and chill at least 1 hour or up to 24 hours. Remove yogurt cheese, if using, from refrigerator. Discard liquid in bowl; set yogurt aside. In a chilled bowl beat cream, powdered sugar, and vanilla until soft peaks form. Fold in yogurt cheese or mascarpone cheese. Cover and chill for 1 hour or up to 4 hours. Divide oranges among 6 dessert dishes. Spoon yogurt mixture on orange sections; drizzle with pomegranate syrup. Sprinkle with pomegranate seeds or orange peel. Makes 6 servings