Melt the butter in a medium heavy-bottomed saucepan over medium heat. Add the brown sugar, cream, and corn syrup and stir until smooth. Bring the mixture to a boil and cook, stirring occasionally, until slightly thickened, about 5 minutes.
Remove from the heat, whisk in the bourbon and espresso, and set aside until slightly cooled, about 20 minutes. Before serving, whisk the sauce until smooth.