This is by far the most labor intensive and complicated recipe I have ever made.
You will need a springform pan with 3 inch sides. I added that you can use a hand held mixer in most of the directions, simply because I do not have a stand mixer, but I do believe it is part of the reason I didn't get the height I wanted. If you use a handheld mixer, I would try doubling the recommend mixing times.
Melt butter, chocolate, and espresso powder in large heatproof bowl set over saucepan filled with 1 inch of barely simmering water. Stir occasionally until smooth. Remove from heat and cool for about five minutes. Get your egg yolks and vanilla, and whisk them in until incorporated.
With a hand held mixer or stand mixer, beat egg whites and salt at medium speed until frothy, about 30 seconds. Add half of brown sugar and beat until combined, about 15 seconds. Add remaining brown sugar and beat at high speed until soft peaks form when whisk is lifted, about 1 minute longer, scraping down sides halfway through.
With a whisk, fold one-third of beaten egg whites into chocolate mixture to lighten. Now get a rubber spatula and fold in remaining egg whites until no white streaks remain.
Melt chopped chocolate in large heatproof bowl set over saucepan filled with 1 inch of barely simmering water, stirring occasionally until smooth.
Using a handheld mixer or a stand mixer with whisk attachment, whip cream, granulated sugar, and salt at medium speed until mixture begins to thicken, about 30 seconds. Increase speed to high and whip until soft peaks form when whisk is lifted, 15 to 60 seconds.
Using whisk, fold one-third of whipped cream into chocolate mixture to lighten. Gently fold in remaining whipped cream until no white streaks remain.
Spoon mousse into spring form pan over cooled cake and gently tap pan on counter 3 times to remove any large air bubbles; gently smooth top with offset spatula. Wipe inside edge of pan with damp cloth to remove any drips. Refrigerate cake at least 15 minutes while preparing top layer.
Place white chocolate in medium bowl. Bring ½ cup cream to simmer in small saucepan over medium high heat. Remove from heat; add gelatin mixture and stir until fully dissolved. Pour cream mixture over white chocolate and whisk until chocolate is melted and mixture is smooth, about 30 seconds. Cool to room temperature, stirring occasionally, 5 to 8 minutes (mixture will thicken slightly)
Using a hand help mixer with whisk attachment or stand mixer, whip remaining cup cream at medium speed until it begins to thicken, about 30 seconds. Increase speed to high and whip until soft peaks form when whisk is lifted, 15 to 60 seconds. I actually did this for about 2 minutes to get soft peaks.
Using whisk, fold one-third of whipped cream into white chocolate mixture to lighten. With rubber spatula, fold remaining whipped cream into white chocolate mixture until no white streaks remain.
Gently pour white chocolate mousse into pan over middle layer. Return cake to refrigerator and chill until set, at least two hours.
To serve cake, run thin knife between cake and side of spring form pan; remove side of pan. Run cleaned knife along outside of cake to smooth sides. Cut into slices and serve.