Melt brown sugar and 4 tablespoons butter in a saucepan over medium heat. Stir until sugar dissolves. Bring to a boil over medium heat; remove from heat. Whisk in cream; blend well. Transfer to a heat-resistant bowl. Cool at room temperature, stirring occasionally.
Place remaining 6 tablespoons butter and cream cheese in a large bowl; beat with a mixer on medium-high speed until smooth. Beat in vanilla and salt. With mixer running, slowly pour in cooled brown sugar mixture; beat until smooth. Add powdered sugar gradually, beating well after each addition until completely smooth. Chill slightly for a firmer texture, stirring occasionally.