Melt the white chocolate in a double boiler over medium heat or in a microwave, stirring every 30 seconds, until smooth. Be careful not to scorch the chocolate.
Place the peppermints in a resealable food storage bag and, using a rolling pin, tap the candies to break into small pieces. Place the crushed candies into a strainer with medium holes and shake over another bowl - only the very large pieces should remain in the strainer. Add the melted chocolate to the small pieces and stir to combine.
Line a baking sheet with waxed paper and pour the chocolate-candy mixture onto the paper. Using a rubber spatula, spread smooth to a thickness of about 1/4-inch. Press the large peppermint pieces onto the top of the mixture and transfer to a refrigerator to firm.
When firm, break the bark into bite-size pieces and place in an attractive serving bowl or package in airtight containers to give as gifts. Serve at room temperature.
This is best refrigerated if kept for any length of time.