Line the bottom of a cookie sheet with wax paper; set aside.
Combine sugar, corn syrup and 1/2 cup water in a small, heavy saucepan. Bring to a boil over medium heat, stirring constantly. Then cook without stirring until mixture reaches 238 degrees F on a candy thermometer, about 20 minutes.
Remove from heat. Quickly add marshmallows and peppermint extract, stirring until marshmallows are dissolved. Stir in walnuts, mixing until well coated.
Pour mixture onto cookie sheet. Separate nuts with 2 forks while still warm. After mixture has completely cooled, nut clusters can be broken apart to separate.
Store in an airtight container at room temperature up to 2 weeks.
