In a small bowl, mix the dulce de leche for about a minute to soften. In a separate bowl, whip the heavy cream until stiff peaks form, being careful not to over-mix. Fold the softened dulce de leche into the whipped cream until smooth.
Chop, break, or grate the peppermint crisp bars into small pieces. (A couple of pulses in a food processor works well too.) Fold half of the peppermint crisp pieces into the cream mixture and set the rest aside.
Line the bottom of a square or rectangular baking dish (such as 7" × 10") with tennis biscuits. Spread half of the cream mixture evenly over the biscuits.
Add another layer of tennis biscuits, followed by the remaining cream mixture. Spread evenly with an offset spatula.
Sprinkle the remaining peppermint crisp over the top and refrigerate for at least 2 hours before serving.