Line a 15x10x1-inch baking pan with parchment paper; set aside. In a large bowl toss the 1 1/4 pounds peaches with 1/4 cup of the Ginger Syrup to coat. Pour peach mixture onto prepared pan. Freeze peaches at least 45 minutes.
In a blender combine frozen peaches, the remaining 1/4 cup Ginger Syrup, the Prosecco, and peach schnapps. Let Prosecco bubbles dissipate. Cover and blend until smooth. Pour mixture into six chilled 8-ounce glasses. If desired, garnish with peach slices.
In a small saucepan combine water, sugar, chopped ginger,freshly squeezed lemon juice, and black peppercorns. Bring to boiling; reduce heat. Simmer, uncovered, until sugar dissolves, stirring frequently. Remove from heat; let cool. Strain syrup through a fine-mesh sieve; discard solids. Transfer syrup to a jar with a tight-fitting lid. Store in the refrigerator for up to 2 weeks.