Place peppermint candy in a heavy-duty freezer bag and cover with a towel. Pound bag with a meat mallet or rolling pin until finely crushed. Set aside. (This can be done in a food processor, if preferred).
Line a small, rimmed baking sheet with parchment paper. If necessary, dampen the bottom of the outer edges of the parchment paper to hold it in place.
In a double broiler, melt the dark chocolate until smooth. Transfer while warm and melted to parchment paper and spread with a plastic spatula until uniformly thick.
Thoroughly clean double broiler before melting the white chocolate. Once smooth, stir in the crushed peppermint pieces until evenly distributed.
Pour the white chocolate mixture on top of the dark chocolate layer. Spread until evenly distributed over the dark chocolate layer. Top with extra peppermint pieces, if desired.
Place baking sheet in the refrigerator for at least 2 hours. Once harden, break peppermint bark into pieces before serving or storing.