Make the spiced simple syrup: Bring sugar, 1 cup water, the peppercorns, cloves, cinnamon stick, star anise, and zest to a boil in a small saucepan. Reduce heat, and simmer 5 minutes. For milder flavor, remove star anise, and discard; simmer 10 minutes more. Remove from heat. Let cool completely. Pour through a sieve into a bowl; discard solids. Syrup can be refrigerated in an airtight container up to 1 month.
Assemble the cocktail: Combine all ingredients in a pitcher. Serve over ice, and top with ginger beer and candied ginger.