Add the chopped dark chocolate, butter, and Kahlua into a bowl. In a double boiler over medium heat, melt together the mixture. (This can also be done in a microwave in 30-second intervals). Set aside to cool slightly.
In a stand mixer or with a hand mixer, add the egg whites and whisk together on medium speed until just foamy. After the egg whites are foamy, add in the sugar and whip until medium peaks form.
Add the gelatin to the water. Mix to combine and set aside to bloom for at least 5 minutes.
While the gelatin is blooming, whip the egg yolks in a bowl with a hand mixer or the base of a stand mixer until they are pale in color. Fold the whipped egg yolks into the chocolate mixture.
After the yolks are added, heat ½ cup of heavy cream in the microwave until warm but not boiling. Add the gelatin-water mixture to the warmed cream and mix to combine. Fold the mixture into the chocolate mixture.
After the gelatin is added, fold the whipped egg whites into the chocolate mixture
Lastly, whip the remaining 1 cup of heavy whipping cream until soft peaks form. Fold the whipped cream into the chocolate mixture until combined.
Pour the mousse over the cooled cake into the springform pan. Spread into an even layer so the top is flat. Cover with a piece of plastic wrap to set for at least 4 hours or overnight.