Finely chop chocolate. In a 1 1/2- to 2-quart saucepan bring cream, sugar, and corn syrup to a boil over moderately low heat, whisking until sugar is dissolved. Remove pan from heat and add chocolate, whisking until chocolate is melted. Cut butter into pieces and add to frosting, whisking until smooth.
Transfer frosting to a bowl and cool, stirring occasionally, until spreadable (depending on chocolate used, it may be necessary to chill frosting to spreadable consistency). I found that stirring this over a bowl of ice water did a great job of cooling it off quickly and evenly.
Spread frosting between cake layers and over top and sides. Cake keeps, covered and chilled, 3 days. Bring cake to room temperature before serving.