Preheat oven to 350 degrees. Butter bottom and sides of two 9-by-2-inch round cake pans. Line pans with parchment paper rounds and butter again. Dust with flour; tap out excess. In a small bowl, sift together flour and cornstarch.
In the bowl of an electric mixer fitted with the whisk attachment, beat egg yolks, vanilla, and 3/4 cup sugar on high speed until thick and pale, about 3 minutes. Transfer egg-yolk mixture to a large bowl. Wash and dry mixer bowl and whisk attachment.
Combine egg whites and salt in mixer bowl, and whisk on medium speed until soft peaks form, about 1 1/2 minutes. With mixer running, slowly add remaining 6 tablespoons sugar; continue whisking until stiff and glossy, about 1 minute more.
Fold egg-white mixture into egg-yolk mixture. In three additions, fold reserved flour mixture into egg mixture. Divide batter between prepared pans, smoothing tops with an offset spatula. Bake until light golden brown and a cake tester inserted in the center comes out clean, about 20 minutes.
Transfer pans to wire racks to cool slightly; turn out cakes, remove parchment paper, and let cool completely.
Using a serrated knife, halve each cake horizontally to form 2 layers. Transfer 1 layer to a serving platter and spread 1 cup frosting evenly on top. Set another cake layer on top, and repeat process with more frosting and remaining cake layers. Spread 1 1/2 cups frosting over entire cake. Refrigerate until firm, about 30 minutes. Spread remaining 2 1/2 cups frosting over cake, smoothing the top and sides. Use a cake comb to give sides of cake a decorative finish, if desired. Serve immediately, or refrigerate up to 2 days; let cake come to room temperature before serving.
For Caramel Buttercream Frosting: Combine 1 1/4 cups sugar and 1/2 cup water in a medium saucepan. Bring to a boil, stirring to dissolve sugar. Brush down sides of pan with a damp pastry brush, and cook, without stirring, until dark amber. Remove from heat, and quickly dip bottom of pan in a bowl of ice water to stop it from cooking further. Gradually stir in cream until caramel is smooth.
Whisk together remaining 1 cup sugar, the egg whites, and salt in a standing mixer bowl set over a pot of simmering water. Whisk until sugar dissolves and mixture is warm. Transfer bowl to a standing mixer fitted with the whisk attachment, and whisk on medium-high speed until fluffy, cool and stiff peaks form, about 10 minutes. Add butter, 2 tablespoons at a time and whisking well after each addition. Whisk in vanilla. Slowly pour in caramel with mixer on medium speed, and whisk until incorporated. Increase to high speed (the mixture will look curdled), and continue to whisk until smooth, about 3 minutes. Switch to the paddle attachment and beat on low speed for 2 minutes. Use immediately, or transfer to an airtight container and refrigerate up to 3 days; bring to room temperature before using, and beat until smooth.
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