Place a metal mixing bowl and the beaters from an electric mixer in the freezer to chill for about 30 minutes.
Remove the bowl and beaters from the freezer. Pour the heavy whipping cream into the chilled bowl. Using the chilled beaters, beat the cream on high speed until stiff peaks form, about 6 minutes.
Gently fold the sweetened condensed milk and vanilla extract into the whipped cream until well combined.
Fold in the crushed Oreo cookies until evenly distributed.
Transfer the mixture to a freezer-safe container. Cover and freeze until firm, about 6 hours or overnight.