Place mixer beaters in a large metal bowl; refrigerate 30 minutes. Cut or tear cake into bite-sized pieces; set aside.
Break white chocolate into smaller pieces; microwave at 70% power, stirring after 45 seconds. Microwave until melted, about 30 seconds more. Stir until smooth. Let stand 5 minutes; stir 1/4 cup heavy cream into white chocolate until smooth.
In the chilled bowl, beat remaining heavy cream until soft peaks form. Gently fold two-thirds of whipped cream into white chocolate. Stir extract into remaining whipped cream.
In a trifle bowl, layer cake and white chocolate mixture, repeating layers. Top with peppermint-flavored whipped cream. Refrigerate, covered, until serving. Sprinkle with crushed candies.
Test Kitchen tip
If you want a touch of color, add a couple of drops of red food coloring.