1In 1-quart saucepan, heat 1/2 cup sugar, water and chopped gingerroot over high heat to boiling. Boil 1 minute to dissolve sugar. Remove from heat. Cool completely, about 20 minutes. Strain out ginger pieces. Pour Ginger Syrup into glass jar.
2In food processor, place Sugar for Rim ingredients. Process with on-and-off pulses until combined. Spread in shallow dish.
3In carafe or pitcher, place all Punch ingredients except ice and orange slices, adding gin and ginger syrup to taste; stir to combine.
4To serve, dip each drinking glass rim into water or wipe with orange wedge; dip into sugar for rim to coat. Fill glasses with ice; pour punch into glasses. Garnish each with orange peel.