Line a baking sheet with foil, shiny-side up; smooth out the creases. Make sure all your tools are dry.
Chop the white chocolate into 1/2-inch pieces with a large knife. Place all but 1 cup of the chopped chocolate in a microwave-safe bowl. Microwave 30 seconds, then stir with a rubber spatula. Continue microwaving and stirring at 30-second intervals until melted, 3 to 5 minutes total. Immediately add the reserved chopped chocolate to the bowl; stir vigorously until melted and shiny. Don't worry if there are a few small unmelted pieces.
Pour the white chocolate onto the prepared baking sheet; use the rubber spatula to spread it into a 10-to-12-inch circle, about 1/4 inch thick.
Press the peppermints and marshmallows into the chocolate, arranging them so each bite has a mix of flavors and textures. Let the bark harden completely at room temperature, about 1 hour. (If the room is warm, you may need to freeze the bark for a few minutes.) Break into pieces and store in an airtight container at room temperature for 1 to 2 weeks.