Bring ginger, 2/3 cup of sugar and 1/2 cup water to a boil in a small saucepan. Reduce to a simmer; cook until liquid thickens to maple syrup consistency, about 15 minutes. Remove from heat; let cool. Strain syrup; discard ginger.
Combine Chinese five-spice powder and remaining 2 tablespoons sugar on a shallow plate. Moisten the rim of Champagne flutes with water and dip in sugar. Drop 1 teaspoon crystallized ginger and 1 star anise into each glass. Add 1 tablespoon syrup and about 3 ounces Champagne.
In a 3 1/2- to 4-quart pan, combine cranberry juice, ginger, cinnamon sticks, and star anise. Boil over high heat until reduced to 2 cups, about 1 hour. Let cool about 30 minutes, then pour through a fine strainer into a small pitcher. Chill syrup until cold, at least 1 1/2 hours.
For each serving, pour 2 tablespoons of the cranberry syrup and 1 teaspoon cognac into a Champagne flute (6 to 8 oz.). Add 1/2 cup (4 oz.) Champagne. Garnish with 2 or 3 cranberries if desired.
