To Make Frosting:

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 (just start with a tablespoon or two), stirring with a wooden spoon until completely smooth. (Be careful, as the mixture will definitely bubble up and possibly splatter a bit as you add in the cream.)  Set aside until cool to the touch, about 25 minutes.

Beat the butter ]in the bowl of a stand mixer fitted with the paddle attachment 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 off the mixer, and then add caramel. Beat frosting on low to combine, and then increase to medium-high and beat until airy and thoroughly mixed, about 2 minutes. Refrigerate if not using immediately (or to harden the frosting a bit).