Add the sugar and water to a large saucepan and bring it to a boil over medium-high heat, stirring the mixture occasionally to get the sugar to dissolve. Once the sugar is dissolved, reduce the heat to medium and don't stir the mixture. Continue to cook the caramel, swirling the pan occasionally to get even caramelization, until the syrup becomes a deep caramel color, about 6 minutes. Being very careful (the caramel is very, very hot) begin adding the cream to the caramel mixture a little at a time (the caramel will furiously bubble up) and whisk until all of the warm cream is added. Whisk in the bourbon and then whisk in the butter.
Cool completely and stir before glazing doughnuts. Extra bourbon caramel sauce can be refrigerated for up to 1 week; warm over low heat before using.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.