Melt the butter in a heavy 2- or 3-quart saucepan over medium-low heat. Add the brown sugar and stir almost constantly with a wooden spoon. After 2 to 3 minutes, the sugar will melt and smooth out, and the mixture will begin to bubble (it's all right if it still looks separated at this point). Once this happens, stir constantly for 2 minutes (less if the sugar smells like it's burning). Carefully add the 1/4 cup cream and stir constantly for another 2 minutes. The mixture will thicken slightly and look smooth and glossy. Remove the pan from the heat and let cool for 5 minutes, stirring frequently. Beat in the confectioners' sugar and vanilla with the wooden spoon. If the frosting seems a little dry, beat in more cream, 1/2 tablespoon at a time, until it's thick, smooth, and spreadable.