Line an 8 x 8 pan with aluminum foil and spray with cooking spray.
Divide the condensed milk in half.
Place half of the condensed milk in a medium saucepan with the dark chocolate chips. Cook over medium heat, stirring constantly until the chocolate is completely melted. Remove from heat and stir in the vanilla.
Pour the dark chocolate mixture into the pan and put the pan in the refrigerator.
Place the other half of the condensed milk in a medium saucepan with the white chocolate chips. Cook over medium heat, stirring constantly until the chocolate is completely melted. Remove from heat and stir in the peppermint extract and half the candy canes.
Pour the white chocolate mixture over top of the dark chocolate mixture and sprinkle with the remaining crushed candy canes.
Allow the fudge to harden completely before cutting into 24 squares.