We use this caramel butttercream in alternating layers of yellow genoise cake to make our rich Dobos Torte.
In a medium, heavy saucepan, bring 1 1/4 cups sugar and the water to a boil over medium-high heat, stirring until sugar dissolves; wash down sides of pan with a pastry brush dipped in water to prevent crystals from forming.
Continue cooking, without stirring, until caramel is dark amber, swirling pan to color evenly. Remove from heat, and carefully pour in heavy cream in a steady stream (it will spatter); stir with a wooden spoon until smooth. Let cool.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter on medium speed until fluffy and pale; set aside. In the heatproof bowl of electric mixer set over a pan of simmering water, gently whisk together remaining cup sugar and the egg whites until mixture is warm to the touch and sugar has dissolved, about 3 minutes.
Attach bowl to mixer fitted with the whisk attachment, and beat on medium speed until mixture is fluffy and cooled, about 10 minutes. Increase speed to high; whisk until stiff peaks form. Reduce speed to medium-low; add butter, 1/4 cup at a time, beating well after each addition. Beat in vanilla.
Switch to the paddle attachment. Add caramel mixture; beat on lowest speed until smooth, 3 to 5 minutes. If using the same day, set aside at room temperature, covered with plastic. Or refrigerate in an airtight container up to 3 days. Before using, bring to room temperature; beat with paddle attachment until smooth.