12 tablespoons unsalted butter (1 1/2 sticks), at room temperature
1/2 teaspoon fine salt
1 cup powdered sugar
Briefly stir together granulated sugar and water in a small saucepan and bring to a boil over medium-high heat. Continue cooking, without stirring, until mixture turns dark amber in color, about 6 to 7 minutes.
Remove from heat and slowly add in cream and vanilla, stirring with a wooden spoon until completely smooth. Set aside until cool to the touch, about 25 minutes.
Combine butter and salt in the bowl of a stand mixer fitted with the paddle attachment and beat on medium-high speed until light in color and fluffy, about 3 minutes. Reduce speed to low, add powdered sugar, and mix until completely incorporated.
Turn mixer off and scrape down the sides of the bowl, then add caramel. Beat frosting on medium-high speed until airy and thoroughly mixed, about 2 minutes. Cover and refrigerate until stiff, about 45 minutes, before using.