In a medium mixing bowl, whisk together pistachio pudding mix with milk for 1–2 minutes until well blended. Refrigerate for 5 minutes.
Using small dessert cups, layer the pudding, cake piece, and a sprinkle of peppermint chips. Repeat for a second layer.
In a small glass microwave-safe bowl, melt the chocolate chips for 60 seconds, stir, and then continue melting at 30 second increments in the microwave until the chips are completely melted, stirring in between each additional 30 seconds.
Drizzle over the top of the individual trifles.
Sprinkle on any remaining peppermint chips.
Top each trifle with a PEEPS® Chick. Serve immediately or cover with plastic wrap and chill in refrigerator.