Place the sugar, corn syrup, and water in a saucepan and stir together. Heat over high, without stirring, until the sugar boils. Continue cooking for about 8 minutes until the caramel turns a medium amber color. At this point, the bubbles will start to settle. Only swirl the pan, do not stir, to evenly distribute the color once it begins to brown.
Once amber in color, promptly remove the saucepan from the heat. While whisking, very carefully pour in the cream. The caramel will bubble and steam, so use caution. Keep whisking until smooth. Add the salt and vanilla. Stir to combine.
Pour the caramel sauce into the bowl of a stand mixer and allow to cool for 10 to 15 minutes. Using the whisk attachment, mix on low speed while adding in the butter, a couple tablespoons at a time. Continue to mix until all of the butter has been added and is incorporated. Turn the mixer to medium-high and whisk for two minutes.
Stop the mixer and add the confectioner’s sugar. Gradually increase the speed from low to medium (making sure sugar doesn’t fly out of the bowl) and mix for a few minutes.
At this point, the caramel will start to lighten in color and thicken in texture but will need to chill before icing the cake. Refrigerate the caramel frosting (in the mixing bowl) for 10 to 15 minutes, until thick and spreadable. Fill and frost the cake immediately.