Adjust oven rack to middle position and heat oven to 350ºF. Butter bottom and sides or line with parchment a 9 ½-inch springform pan. Melt butter, chocolate and espresso powder in a large bowl set over a saucepan filled with 1-inch of barely simmering water, stirring occasionally until smooth. Remove from the heat and cool for 5 minutes. Whisk in the egg yolks and vanilla.
In a stand mixer fitted with the whisk attachment, beat egg whites and salt until frothy. Add half the white sugar and beat until combined. Add the remaining sugar and beat at high speed until soft peaks form. Using rubber spatula fold half of egg whites into chocolate mixture to lighten. Fold in remaining egg whites until no white streaks remain. Pour into prepared pan and smooth with offset spatula. Bake until edges are set and middle is soft, 13-18 minutes. Transfer to a rack and cool completely in pan, about 1 hour.
Combine cocoa powder and hot water in a small bowl, set aside. Melt chocolate in a large bowl set over a saucepan filled with 1-inch of barely simmering water, stirring occasionally until smooth. Remove from heat and cool for 5 minutes.
In a clean bowl of a stand mixer fitted with whisk attachment, whip cream, sugar, and salt at medium speed for 30 seconds. Increase speed to high and whip until soft peaks form, about 1 minute.
Whisk cocoa powder mixture into melted chocolate. Using rubber spatula, fold half the whipped cream into chocolate mixture. Add the remaining whipped cream and fold until no white streaks remain. Spoon mousse into pan over cooled cake and gently rap on the counter to remove any air bubbles. Spoon the top with an offset spatula. Clean the sides to remove any drips or smears. Refrigerate for at least 15 minutes.
In a small bowl, sprinkle gelatin over water; let the stand at least 5 minutes. Place white chocolate chips in a medium bowl. Bring ½ cup cream to a simmer in a small pan over medium heat. Remove, add gelatin mixture and stir until dissolved. Pour hot cream over white chocolate chips and stir until chocolate is melted. Cool to room temperature, about 5-10 minutes.
In a clean bowl of stand mixer fitted with the whisk attachment, whip remaining cream at medium speed for 30 seconds. Increase the speed to high and whip until soft peaks form, 1 minute. Using rubber spatula fold half the cream into the white chocolate mixture. Add the remaining cream and fold until no white chocolate streaks remain. Spoon white chocolate mousse into prepared pan over middle layer and smooth with offset spatula. Return cake to refrigerator and chill until set, at least 2 ½ hours.
Garnish Top of cake with chocolate curls or dust with cocoa. For neat slices, dip a thin knife in hot water or use dental floss (non-flavored) to cut the cake. Enjoy!