In a standing mixer fitted with a whisk attachment (or a large bowl with a handheld electric mixer), cream together sugar and butter. Mix on low until well blended and then blend on medium and beat for another 3 minutes or so, until smooth.
Add vanilla and 1 tablespoon whipping cream and continue to beat on medium speed for 1 minute more, if frosting seems dry, add remaining tablespoon of cream and blend until smooth.