Melt the white chocolate melts in the microwave in 30-second bursts. Stir after each round until smooth and completely melted. Add the peanut butter to the melted white chocolate, and stir until smooth.
Scoop the cookies onto the prepared baking sheets with a 1-tablespoon cookie scoop or a spoon. They will be sticky and messy, and this is OK. Add extra toppings, if desired. Refrigerate for 30-45 minutes, or until the white chocolate mixture is set.
Once the avalanche cookies are chilled, transfer to an airtight container for storage. If layering the cookies, place a sheet of wax paper between the layers. Store in the refrigerator for up to 5 days.