To make the ginger simple syrup, add sugar, water, and ginger pieces to a small saucepan. Heat until the sugar has dissolved. Let cool completely and strain out ginger pieces. Set aside.
To make the cocktail, add frozen peaches, orange liqueur, ginger syrup, and Ohza Classic Bellini to a blender.
Purée until smooth.
Pour into champagne glasses or rocks glasses and garnish with peach slices.