Divide the melted white chocolate into 2 containers and dye one batch red. Spoon the chocolate into a square silicone mold to create the chocolate shells, making half of the squares white and half red. Place the mold into the freezer for the chocolate to harden.
Pour the hot cream on top of the white chocolate and mix well. Place the bowl on top of a bowl filled with ice water and mix until the ganache thickens. Add the peppermint extract and candy canes and combine. Place the ganache in a piping bag fitted with a round tip.
Pipe the ganache into the chocolates and pour more melted chocolate on top. Return the chocolates to the freezer for the chocolate to fully harden, about 30 minutes.
Unmold the chocolates and using a toothpick, draw ribbons and bows onto the chocolates. Draw red bows onto the white boxes and white bows onto the red boxes. Return to the freezer for a final 10 minutes to set and enjoy!