In a double boiler, melt the chopped dark chocolate, butter, and Kahlua over medium heat. Set aside to cool slightly.
In a stand mixer, whip the egg whites on medium speed until foamy. Gradually add the sugar and whip until medium peaks form.
Bloom the gelatin in the water for at least 5 minutes.
Whip the egg yolks until pale and fold them into the chocolate mixture.
Warm 1/2 cup of heavy cream and mix in the gelatin. Fold this into the chocolate mixture.
Fold the whipped egg whites into the chocolate mixture.
Whip the remaining 1 cup of heavy cream to soft peaks and fold into the chocolate mixture.
Pour the mousse over the cooled cake in the springform pan. Spread evenly and cover with plastic wrap. Chill for at least 4 hours or overnight.