1. Combine half-and-half, butter, and corn syrup in a medium saucepan over medium-high heat. Bring to a boil; cook 1 minute, stirring frequently. Remove from heat; add chocolate and peppermint extract, stirring until smooth and creamy. Pour chocolate mixture into a shallow dish; cover and chill overnight.
2. Place cocoa in a shallow dish. Scoop chocolate mixture by teaspoonfuls; shape into 40 balls using hands. Roll balls in cocoa, and place on wax paper. Store in refrigerator until ready to serve.