Simmer water, 1/2 cup sugar and sliced ginger in a small saucepan for 10 minutes. Remove the saucepan from heat and stir in vodka. Chill for 2 hours or overnight. When ready to serve, strain to remove the ginger pieces.
Spread the sugar into a thin layer on a plate. Coat the rim of the glass with the juice from the lemon wedge and immediately dredge in the plate of sugar.
Add a few pieces of candied ginger to each glass. Pour 1 tablespoon of the ginger-infused simple syrup over the ginger pieces and top with the sparkling wine until the glass is 2/3 full.