Combine corn syrup, sugar, and water in a saucepan. Cook over medium heat, stirring constantly, until mixture comes to a boil. Continue cooking to softball stage, about 238°F on a candy thermometer, or until a small amount of mixture forms a soft ball when tested in very cold water.
Remove from heat, add peppermint and marshmallow. Stir until dissolved. Add Nature's Eats Chopped Walnuts or Nature's Eats Pecan Pieces; stir until well coated. Pour onto waxed paper. Separate nuts whiles still warm.
Makes about 1¼ pounds of minted walnuts or pecans.