In a heavy, medium saucepan, combine the sugar and 1/3 cup water and cook over medium-high heat, carefully swirling the pan (do not stir) until the sugar dissolves. Cover the saucepan and boil for 2 minutes. Uncover and continue cooking, swirling occasionally, until the liquid darkens, about 6 minutes. Carefully stir in 1 cup heavy cream; set the caramel sauce aside.
Using an electric mixer, beat the remaining 1/4 cup heavy cream until stiff peaks form.
In a small saucepan, heat the milk and 1/4 cup reserved caramel sauce over medium heat, stirring, until hot. Pour into 2 serving mugs and let stand for 1 minute. Stir 3 tablespoons scotch into each mug. Top with the whipped cream and drizzle with the remaining caramel sauce.