Line an 8x8-inch baking pan with parchment paper, allowing some overhang on the sides for easy removal. Set aside.
In a large mixing bowl, combine the softened cream cheese and powdered sugar. Use an electric mixer to beat until smooth and creamy, with no lumps remaining.
Pour in the sweetened condensed milk and vanilla extract. Continue beating until the mixture is fully combined and smooth.
In a microwave-safe bowl, melt the white chocolate chips in 20-second intervals, stirring between each, until completely smooth. Be careful not to overheat.
Gradually add the melted white chocolate to the cream cheese mixture, beating as you pour. The mixture should be thick, creamy, and glossy.
Gently fold in the crushed chocolate sandwich cookies and a pinch of salt using a spatula. Distribute the cookie pieces evenly throughout the fudge batter.
Pour the fudge mixture into the prepared pan, spreading it evenly with the spatula. Chill in the refrigerator for at least 3 hours or until fully set.
Once firm, use the parchment paper overhang to lift the fudge from the pan. Cut into small squares and serve. Store leftovers in an airtight container in the fridge.