Line an 8x8-inch baking pan with nonstick foil or parchment, leaving an overhang for easy removal; set aside.
Split the 14 ounces sweetened condensed milk evenly between two microwave-safe bowls (about 7 oz each). Set both bowls aside.
In one bowl, combine the white chocolate chips and 2 tablespoons butter with one portion of the sweetened condensed milk. Microwave for 30 seconds, stir, then continue microwaving in 15–30 second bursts, stirring between, until smooth and fully melted.
Stir the chopped Oreos into the white chocolate mixture until evenly distributed, then spread this mixture into the prepared pan in an even layer.
In the second bowl, combine the semi-sweet chocolate chips with the remaining sweetened condensed milk. Microwave in 20–30 second bursts, stirring frequently, until smooth and fully melted.
Pour the melted semi-sweet chocolate mixture evenly over the Oreo white-chocolate layer and smooth the top with a spatula.
Refrigerate the pan until the fudge is fully set, about 1–2 hours, then lift out using the foil overhang and cut into squares.