Line a baking sheet with parchment paper. This will prevent sticking.
In a bowl, combine peanut butter and white chocolate chips. Microwave on low, stirring often, until melted and smooth.
Pour the melted mixture into a piping bag and twist it closed. Let it cool for 5 minutes, then snip a small opening in the tip.
Place the fudge striped cookies striped side down on the baking sheet. Pipe a small circle of the melted mixture onto the center of each cookie.
Top each cookie with a miniature peanut butter cup, placing it upside down (larger side down) on the piped circle. Gently press it down.
Add an M&M to the "hatband" to create a buckle.
Let the pilgrim hats set completely before serving, or chill for 10-15 minutes to speed up the process.
Notes
Be careful not to overheat the peanut butter and white chocolate. If it gets too hot, it can seize up and become grainy. Stir frequently and use short bursts in the microwave.