Melt 4 Tbsp (57g) butter and remove from heat. Whisk in 2 oz finely chopped or shredded dark chocolate and 2 tsp corn syrup until chocolate is melted and smooth.
For the bottom layer:
heat oven to 325 degrees. Grease 9 ½” springform pan. Combine butter, chocolate, and espresso powder and heat until melted, stirring often. Let cool about 5 minutes. Whisk in egg yolks and vanilla.
Whip egg whites, cream of tartar, and salt on medium-low speed until foamy. Add half of sugar and whip until combined. Add remaining sugar, increase speed to high, and whip until soft peaks form. fold one-third of beaten egg whites into chocolate mixture to lighten. Using rubber spatula, fold in remaining egg whites until no white streaks remain. Carefully transfer batter to pan and smooth top with spatula
Bake until cake is firm around edges and center springs back when pressed gently, 13 to 18 minutes. Let cake cool completely in pan before adding top layer
For the top layer:
Combine hot water and cocoa in small bowl; set aside. Melt chocolate. Let cool slightly, 3-5 minutes
Whip cream, sugar, and salt on medium-low speed until foamy. Increase speed to high and whip until soft peaks form.
Whisk cocoa mixture into melted chocolate until smooth. Fold one-third of whipped cream into chocolate mixture to lighten. Using rubber spatula, fold in remaining whipped cream until no white streaks remain. Spoon mousse into pan over cooled cake, smooth top with offset spatula, and gently tap pan to release air bubbles.
Refrigerate cake until set, 3 hours or up to 2 days.
Run thin knife between cake and side of pan; remove side of pan. Run hot clean knife along outside of cake to smooth. Garnish top of cake with ganache and shaved chocolate if desired. Serve.