Cover a cookie sheet with wax paper. Place the white chocolate in a microwave-safe bowl and microwave until melted, stirring every 30 seconds until smooth. Mix 3/4 cup of the peppermint pieces with the white chocolate and transfer to the baking sheet, spreading the mixture evenly. Sprinkle additional peppermint pieces on top and allow to sit until hard, about 1 hour. Break into pieces and package for gifts.