Line an 8x8 or 9x9 inch pan with parchment paper; set aside.
Set out two microwave-safe bowls and evenly divide the sweetened condensed milk between the two bowls (about ⅔ cup each).
To one of the bowls of sweetened condensed milk, add the chocolate chips; stir. Microwave on 50% power for 45 seconds; stir. If not completely melted, heat in 15 second intervals until smooth.
Pour chocolate mixture into the prepared pan, spread to an even layer and set aside. (If it's really thick, you can use another piece of parchment paper or waxed paper to press it into the pan).
Add white chocolate chips to the other bowl; stir. Microwave on 50% power for 45 seconds; stir. If not completely melted, heat in 15 second intervals until smooth.
Stir in the peppermint candy pieces and the peppermint extract (if using).
Pour the peppermint mixture over the chocolate layer.
Sprinkle additional peppermint candy pieces on top, pressing them in gently.
Refrigerate for 1 hour or until set; cut into squares and enjoy.