In a heavy, medium saucepan, cook the granulated sugar over moderately high heat, stirring occasionally, until melted. Continue to cook, without stirring, until an amber caramel forms, about 3 minutes. Remove from the heat. Add the light brown sugar and stir until smooth. Return the caramel to the heat and carefully add the port; the caramel will harden slightly. Cook, stirring, until the sugar dissolves. Add the cream and cook, stirring occasionally, until thickened, about 6 minutes. Remove from the heat and stir in the vanilla. Transfer the sauce to a pitcher and serve warm.