Place parchment paper in the bottom and up the sides of a 9 x 9 baking dish. Sprinkle half of the peppermint chunk in the bottom of the pan. Set aside.
Create a double boiler by putting water in a medium sauce pan and bringing it to a boil. Place a medium mixing bowl on top of it, being careful it doesn't touch the water.
Place the condensed milk, butter, and peppermint extract in the bowl. Mix well.
Add the milk chocolate chips and white chocolate chips in the bowl. Stir the chocolate mixture until it begins to melt. Stir until melted completely, about 5 minutes.
Add in the salt and mix well.
Pour the fudge into the prepared dish. Smooth the top with a rubber spatula. Sprinkle the remaining peppermint chunks on top and refrigerate for 4 hours or over night.
When ready to cut simply lift the fudge out by the parchment paper. Place on a cutting board and cut into 24 squares.