Step 1Cut the orange rind to obtain two long, thin spirals of peel. Set aside the orange flesh for another use.
Step 2Place a sugar cube on top of the opened bottle of bitters. Turn the bottle over to saturate the cube, then place the soaked cube in the bottom of a Champagne flute. Repeat with the second sugar cube, placing it in the other glass.
Step 3Add one-half ounce Cointreau and one-half ounce Cognac to each glass. Swirl to mix. Fill each glass with Champagne. Garnish each with an orange spiral.