Add ¼ cup butter, 3 Tbsp. cola soft drink, and 2 ½ Tbsp. unsweetened cocoa in a 2-qt. saucepan over medium-low heat, stirring constantly, until butter melts.
Remove from heat; stir in 1 Tbsp. bourbon.
Beat in 2 cups plus 2 Tbsp. powdered sugar at medium speed with an electric mixer until smooth.