In a medium microwave-safe bowl, combine the semisweet chocolate chips and milk chocolate chips. Microwave on high power for 1 minute; then remove and stir.
Return the bowl to the microwave and cook on 50% power for 1 minute longer; remove and stir again. Continue microwaving at 50% power and stirring until the chips are melted and the mixture is completely smooth.
Remove the bowl from the microwave and stir in the chocolate mint candies until smooth. Add peppermint extract and stir until combined.
Dip the cookies, one at a time, into the chocolate mixture. I drop them into the chocolate, then remove them with a fork. Gently shake off the excess chocolate and place each on waxed paper to cool and set. Store in cool place in an airtight container at room temperature.