Step 1

Fill a small saucepan with water to a depth of 1 inch, and bring to a simmer over medium. Combine chocolate and butter in a medium heatproof bowl; set bowl over pan of water, ensuring bottom of bowl doesn't touch water. Heat, stirring often, until melted and smooth, about 5 minutes. Remove from heat; cool slightly, about 10 minutes.

Step 2

Vigorously whisk together egg yolks, kosher salt, and ¼ cup of the granulated sugar in a large bowl until pale and thickened, about 3 minutes. Gradually stream in cooled chocolate mixture, whisking constantly until well combined. Whisk in vanilla and almond extracts. Set aside.

Step 3

Beat egg whites with a stand mixer fitted with a whisk attachment on medium speed until frothy, about 45 seconds. With mixer running on medium speed, gradually add ¼ cup of the sugar, beating until stiff peaks form, about 2 minutes. Gently fold egg white mixture into chocolate mixture in 3 additions.

Step 4

Beat 1 cup of the heavy whipping cream with stand mixer fitted with whisk attachment on medium speed until stiff peaks form, about 1 to 2 minutes. Fold whipped cream into chocolate mixture.

Step 5

Lightly grease a 9-inch springform pan with butter. Arrange half of ladyfingers in a single layer on bottom of pan, breaking cookies as needed. Spread half of chocolate mixture (about 3½ cups) in an even layer on top of cookies. Sprinkle with ½ cup sliced almonds. Repeat layering with remaining ladyfingers, chocolate mixture, and ½ cup almonds. Cover and chill overnight, about 12 hours.

Step 6

Just before serving, beat remaining 1½ cups whipping cream with stand mixer fitted with whisk attachment on medium-high speed until frothy, about 30 seconds. Gradually add remaining 2 tablespoons sugar, beating until soft peaks form, 1 to 2 minutes.

Step 7

Run a small offset spatula around edges of pan to loosen. Remove sides of pan, and smooth sides of cake with spatula. Top cake with whipped cream; spread in an even layer. Dust lightly with cocoa, and garnish with additional toasted sliced almonds.