Stir the sugar and water in a large saucepan over medium heat until the sugar dissolves, about 5 minutes. Cool completely.
Puree the peaches and orange peel in a blender with 1 1/2 cups of the sugar syrup until smooth. Strain through a fine-meshed strainer and into a bowl. Transfer the puree into a pitcher or clear glass bowl.
For each serving, pour 2 to 4 tablespoons of the peach puree into a Champagne flute. Slowly pour enough Prosecco into the flute to fill. Gently stir to blend. Garnish each with an orange peel twist, and serve.
Do-Ahead Tip: The peach puree can be made 1 day ahead. Cover and refrigerate.
Recipe courtesy Giada De Laurentiis