In a 2 or 3 quart heavy saucepan, melt butter over med-low heat. Add brown sugar and stir almost constantly. After 2-3 minutes the sugar will melt and smooth out, and the mixture will begin to bubble (it may look separated). Once this happens, stir constantly 2 minutes (less if sugar smells like it is burning).
Carefully add the cream and stir constantly for 2 minutes. The mixture will thicken slightly and will look smooth and glossy. Remove pan from heat and let cool 5 minutes, stirring frequently. Beat in the powdered sugar and vanilla. If the frosting seems a little dry, beat in more cream, 1/2 TBS at a time, until it is thick, smooth and spreadable.