Prepare an ice-water bath. In a medium saucepan, bring 1 1/4 cups sugar and 1/2 cup water to a boil, stirring until sugar has dissolved. Brush down sides of pan with a damp pastry brush, and cook, without stirring, until dark amber. Immediately dip bottom of pan in ice-water bath to stop the cooking. Gradually stir in cream until completely smooth.
Combine remaining 1 cup sugar, egg whites, and salt in the bowl of a stand mixer set over (not in) a pot of simmering water. Whisk constantly until sugar has dissolved, and mixture is warm and feels completely smooth when rubbed between fingertips. Transfer bowl to mixer fitted with the whisk attachment. Beat on medium-high speed until stiff peaks form and bottom of bowl is cool to the touch, about 10 minutes.
Add butter, 2 tablespoons at a time, beating well after each addition. Beat in vanilla. Reduce speed to low and slowly beat in caramel until incorporated. Increase speed to high (mixture will look curdled) and continue beating until smooth, about 3 minutes. Switch to paddle attachment and beat on low, 2 minutes more. Use immediately, or transfer to an airtight container and refrigerate up to 3 days. Before using, return to room temperature and beat until smooth.