Line a 8 or 9-inch square pan with parchment paper or foil. Leave one or two inches of paper sticking out of the pan.
In a medium saucepan over low heat, melt 2 1/4 cups of the white chocolate chips (reserve 1/4 cup) with the sweetened condensed milk. Stir frequently to prevent it from sticking to the bottom of the pan and burning.
Once the chips are melted and the mixture is combined, stir in the vanilla extract. Add the chopped Oreos and stir until combined.
Spread into prepared pan and sprinkle with reserved white chocolate chips and semi-sweet chocolate chips. Press them in lightly so they will stick.
Chill fudge in the freezer for two hours or more until it is fully firmed up. Lift fudge out of the pan by gripping the edges of the parchment paper. Slice (might want to make them small–they are rich!) and serve at room temperature. Store in fridge or freezer.