Line an 8x8-inch baking pan with parchment paper, leaving overhang on two sides for easy removal.
In a medium saucepan over low heat, combine the white chocolate chips, sweetened condensed milk, and butter. Stir constantly until completely melted and smooth, about 5 minutes.
Remove from heat and stir in the vanilla extract and salt. Fold in about 15 of the crushed Oreos until evenly distributed.
Pour the fudge into the prepared pan and spread evenly. Press the remaining crushed Oreos into the top. Refrigerate for at least 2 hours until firm, then lift out and slice into squares.
Notes
Keep the heat low when melting the white chocolate to prevent it from seizing. If it starts to look grainy, add a tablespoon of cream and stir vigorously. Store in the refrigerator for up to 2 weeks in an airtight container.