Sprinkle the gelatin over the cold water in a small bowl. Let sit for 10 minutes, until the gelatin softens.
Meanwhile, pour the Champagne, Cognac, and vanilla into a measuring cup.
Combine the melted chocolates in a medium bowl. Combine the cream, softened gelatin, and corn syrup and pour over the chocolates and, using a small silicone spatula, stir the mixture in one direction, concentrating on the center, until the ganache is smooth and glistening.
Slowly pour the Champagne into the ganache, whisking constantly (if you add the Champagne too quickly, the ganache will separate). Add the butter and stir until it is completely melted, about 1 minute. Put the ganache in the coolest part of your kitchen and let set, stirring occasionally, until spreadable, for about 1 hour before using.
Leftover ganache can be covered and refrigerated for up to 2 weeks; see instructions below.