Place sugar in medium saucepan and heat to medium. Stir occasionally with a silicone spatula (make sure it can handle high heat temps!). As the caramel begins to liquefy, scrape from the bottom and mix back into the granulated pieces. The sugar will clump but eventually it will melt again and turn a deep amber brown. Make sure you are still stirring so it does not burn.
Once the sugar is melted, add butter and stir until butter is melted, about 2-3 minutes. Use a whisk to incorporate the butter with the sugar.
Very, very slowly, add the cream to the sugar mixture while whisking. The mixture will start to bubble violently, but keep stirring and it will calm down. Allow it to boil for 1 minute.
Remove from heat and stir in the salt. Transfer to storage container (such as a mason jar) and allow it too cool for at least 30 minutes before using.
Once the caramel has cooled down, carve out a 1-inch circle about 1/3 through the cupcake from the center of the cupcakes and discard cake pieces. Fill the centers with about a teaspoon of caramel sauce. Set aside and then make the frosting.