Place chocolate morsels and cream in a heavy saucepan. Cook over low heat, stirring constantly with a rubber spatula, until combined and thickened, between 20 and 25 minutes. Increase the heat to medium low; cook, stirring, 3 minutes more. Remove pan from heat.
Stir in corn syrup. Transfer frosting to a large metal bowl. Chill until cool enough to spread, about 2 hours, checking and stirring every 15 to 20 minutes. Use immediately.