Place a 9” x 5” loaf pan or other similarly sized container in the freezer.
Using an electric mixer on medium speed, beat together the condensed milk, cream cheese, and vanilla until thoroughly combined and smooth.
Place the cream in a separate bowl. Use an electric mixer with a whisk attachment to whip the cream at medium-high speed until stiff peaks form.
Fold about a quarter of the whipped cream into the cream cheese mixture, and then gently fold in the remaining whipped cream. Stir in the cookie pieces, saving a handful for scattering over the top if you like.
Transfer the ice cream to the cold pan. If you reserved any cookie pieces, sprinkle them over the top. Cover and freeze at least 5 hours before serving.
Notes
Store in an airtight container in the freezer up to 2 weeks.