Crush the Oreo Cookies in a Ziploc bag until the cookies are in small to medium chunks. Set aside.
Chop the white chocolate or break it into small chunks (or use white couverture chocolate drops).
Add the sweetened condensed milk to a microwave safe bowl and heat in the microwave on 30-50% power for 20 to 30-second increments, stirring well after each increment, until hot.
To make it on the stovetop, add the sweetened condensed milk to a non-stick saucepan and heat it until very warm but not boiling. Remove it from the heat.
Add the chopped chocolate to the hot milk and stir gently with a silicone spatula, just until the chocolate is melted and everything is combined.
Add about 2/3 of the Oreo Cookie crumbs into the mixture and stir to distribute them throughout the mixture.
Press the fudge mixture into an 8-inch by 8-inch square baking pan lined with parchment paper.
Sprinkle the remaining Oreo Cookie crumbs onto the top of the fudge and press them into the top lightly.
Refrigerate for at least 2 hours or overnight before slicing.
Store in the fridge in an airtight container until ready to serve.